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Opening Range Gaps [TakingProphets]What is an Opening Range Gap (ORG)? In ICT, the Opening Range Gap is defined as the price difference between the previous session’s close (e.g., 4:00 PM EST in U.S. indices) and the current day’s open (9:30 AM EST). That gap is a liquidity void—an area where no trading occurred during regular hours. Why ICT Traders Care About ORG Liquidity Void (Gap Fill Logic) -Because the gap is an untraded area, it naturally acts as a draw on liquidity. -Price often seeks to rebalance by retracing into or fully filling this void. Premium/Discount Sensitivity -Once the ORG is defined, ICT treats it as a mini dealing range. -Above EQ (Consequent Encroachment) = algorithmic premium (sell-sensitive). -Below EQ = algorithmic discount (buy-sensitive). -Price reaction at these levels gives a precise read on institutional intent intraday. Support/Resistance from ORG -If the session opens above prior close, the gap often acts as support until violated. -If the session opens below prior close, the gap often acts as resistance until reclaimed. Key ICT Concepts Anchored to ORG Consequent Encroachment (CE): The midpoint of the gap. The algo is highly sensitive to CE as a decision point: reject → continuation; reclaim → reversal. Draw on Liquidity (DoL): Price is algorithmically “pulled” toward gap fills, CE, or the opposite side of the ORG. Order Flow Confirmation: If price ignores the gap and runs away from it, this signals strong institutional order flow in that direction. Confluence with Other Tools: FVGs, OBs, and HTF PD arrays often overlap with ORG levels, strengthening setups. Practical Application for Traders Bias Formation: Use ORG EQ as a line in the sand for intraday bias. If price trades below ORG EQ after the open → look for short setups into the prior day’s low or external liquidity. If price trades above ORG EQ → favor longs into highs/liquidity pools. Execution Framework: Wait for liquidity raids or market structure shifts at ORG edges (.00, .25, .50, .75). Target: EQ, opposite quarter, or full gap fill. Precision Reads: ORG lines let traders anticipate where algorithms are likely to respond, providing mechanical invalidation and clear targets without clutter.
Chỉ báo Pine Script®
của TakingProphets
Quantile-Based Adaptive Detection🙏🏻 Dedicated to John Tukey. He invented the boxplot, and I finalized it. QBAD (Quantile-Based Adaptive Detection) is ‘the’ adaptive (also optionally weighted = ready for timeseries) boxplot with more senseful fences. Instead of hardcoded multipliers for outer fences, I base em on a set of quantile-based asymmetry metrics (you can view it as an ‘algorithmic’ counter part of central & standardized moments). So outer bands are Not hardcoded, not optimized, not cross-validated etc, simply calculated at O(nlogn). You can use it literally everywhere in any context with any continuous data, in any task that requires statistical control, novelty || outlier detection, without worrying and doubting the sense in arbitrary chosen thresholds. Obviously, given the robust nature of quantiles, it would fit best the cases where data has problems. The thresholds are: Basis: the model of the data (median in our case); Deviations: represent typical spread around basis, together form “value” in general sense; Extensions: estimate data’s extremums via combination of quantile-based asymmetry metrics without relying on actual blunt min and max, together form “range” / ”frame”. Datapoints outside the frame/range are novelties or outliers; Limits: based also on quantile asymmetry metrics, estimate the bounds within which values can ‘ever’ emerge given the current data generating process stays the same, together form “field”. Datapoints outside the field are very rare, happen when a significant change/structural break happens in current data-generating process, or when a corrupt datapoint emerges. … The first part of the post is for locals xd, the second is for the wanderers/wizards/creators/: First part: In terms of markets, mostly u gotta worry about dem instruments that represent crypto & FX assets: it’s either activity hence data sources there are decentralized, or data is fishy. For a higher algocomplexity cost O(nlong), unlike MBAD that is 0(n), this thing (a control system in fact) works better with ishy data (contaminated with wrong values, incomplete, missing values etc). Read about the “ breakdown point of an estimator ” if you wanna understand it. Even with good data, in cases when you have multiple instruments that represent the same asset, e.g. CL and BRN futures, and for some reason you wanna skip constructing a proper index of em (while you should), QBAD should be better put on each instrument individually. Another reason to use this algo-based rather than math-based tool, might be in cases when data quality is all good, but the actual causal processes that generate the data are a bit inconsistent and/or possess ‘increased’ activity in a way. SO in high volatility periods, this tool should provide better. In terms of built-ins you got 2 weightings: by sequence and by inferred volume delta. The former should be ‘On’ all the time when you work with timeseries, unless for a reason you want to consciously turn it off for a reason. The latter, you gotta keep it ‘On’ unless you apply the tool on another dataset that ain’t got that particular additional dimension. Ain’t matter the way you gonna use it, moving windows, cumulative windows with or without anchors, that’s your freedom of will, but some stuff stays the same: Basis and deviations are “value” levels. From process control perspective, if you pls, it makes sense to Not only fade or push based on these levels, but to also do nothing when things are ambiguous and/or don’t require your intervention Extensions and limits are extreme levels. Here you either push or fade, doing nothing is not an option, these are decisive points in all the meanings Another important thing, lately I started to see one kind of trend here on tradingview as well and in general in near quant sources, of applying averages, percentiles etc ‘on’ other stationary metrics, so called “indicators”. And I mean not for diagnostic or development reasons, for decision making xd This is not the evil crime ofc, but hillbilly af, cuz the metrics are stationary it means that you can model em, fit a distribution, like do smth sharper. Worst case you have Bayesian statistics armed with high density intervals and equal tail intervals, and even some others. All this stuff is not hard to do, if u aint’t doing it, it’s on you. So what I’m saying is it makes sense to apply QBAD on returns ‘of your strategy’, on volume delta, but Not on other metrics that already do calculations over their own moving windows. ... Second part: Looks like some finna start to have lil suspicions, that ‘maybe’ after all math entities in reality are more like blueprints, while actual representations are physical/mechanical/algorithmic. Std & centralized moments is a math entity that represents location, scale & asymmetry info, and we can use it no problem, when things are legit and consistent especially. Real world stuff tho sometimes deviates from that ideal, so we need smth more handy and real. Add to the mix the algo counter part of means: quantiles. Unlike the legacy quantile-based asymmetry metrics from the previous century (check quantile skewness & kurtosis), I don’t use arbitrary sets of quantiles, instead we get a binary pattern that is totally geometric & natural (check the code if interested, I made it very damn explicit). In spirit with math based central & standardized moments, each consequent pair is wider empathizing tail info more and more for each higher order metric. Unlike the classic box plot, where inner thresholds are quartiles and the rest are based on em, here the basis is median (minimises L1), I base inner thresholds on it, and we continue the pattern by basing the further set of levels on the previous set. So unlike the classic box plot, here we have coherency in construction, symmetry. Another thing to pay attention to, tho for some reason ain’t many talk about it, it’s not conceptually right to think that “you got data and you apply std moments on it”. No, you apply it to ‘centered around smth’ data. That ‘smth’ should minimize L2 error in case of math, L1 error in case of algo, and L0 error in case of learning/MLish/optimizational/whatever-you-cal-it stuff. So in the case of L0, that’s actually the ‘mode’ of KDE, but that’s for another time. Anyways, in case of L2 it’s mean, so we center data around mean, and apply std moments on residuals. That’s the precise way of framing it. If you understand this, suddenly very interesting details like 0th and 1st central moments start to make sense. In case of quantiles, we center data around the median, and do further processing on residuals, same. Oth moment (I call it init) is always 1, tho it’s interesting to extrapolate backwards the sequence for higher order moments construction, to understand how we actually end up with this zero. 1st moment (I call it bias) of residuals would be zero if you match centering and residuals analysis methods. But for some reason you didn’t do that (e.g centered data around midhinge or mean and applied QBAD on the centered data), you have to account for that bias. Realizing stuff > understanding stuff Learning 2981234 human invented fields < realizing the same unified principles how the Universe works ∞
Chỉ báo Pine Script®
của gorx1
3
RVol+ Enhanced Relative Volume Indicator📊 RVol+ Enhanced Relative Volume Indicator Overview RVol+ (Relative Volume Plus) is an advanced time-based relative volume indicator designed specifically for swing traders and breakout detection. Unlike simple volume comparisons, RVol+ analyzes volume at the same time of day across multiple sessions, providing statistically significant insights into institutional activity and breakout potential. 🎯 Key Features Core Volume Analysis Time-Based RVol Calculation - Compares current cumulative volume to the average volume at this exact time over the past N days Statistical Z-Score - Measures volume in standard deviations from the mean for true anomaly detection Volume Percentile - Shows where current volume ranks historically (0-100%) Sustained Volume Filter - 3-bar moving average prevents false signals from single-bar spikes Breakout Detection 🚀 Confirmed Breakouts - Identifies price breakouts validated by high volume (RVol > 1.5x) ⚠️ False Breakout Warnings - Alerts when price breaks key levels on low volume (high failure risk) Multi-Timeframe Context - Weekly volume overlay prevents chasing daily noise Advanced Metrics OBV Divergence Detection - Spots bullish/bearish accumulation/distribution patterns Volume Profile Integration - Identifies institutional positioning Money Flow Analysis - Tracks smart money vs retail activity Extreme Volume Alerts - 🔥 Labels mark unusual spikes beyond the display cap Visual Intelligence Smart Color Coding: 🟢 Bright Teal = High activity (RVol ≥ 1.5x) 🟡 Medium Teal = Caution zone (RVol ≥ 1.2x) ⚪ Light Teal = Normal activity 🟠 Orange = Breakout confirmed 🔴 Red = False breakout risk Comprehensive Stats Table: Current Volume (formatted as M/K/B) RVol ratio Z-Score with significance Volume percentile Historical average and standard deviation Sustained volume confirmation 📈 How to Use For Swing Trading (1D - 3W Holds) Perfect Setup: ✓ RVol > 1.5x (bright teal) ✓ Z-Score > 2.0 (⚡ alert) ✓ Percentile > 90% ✓ Sustained = ✓ ✓ 🚀 Breakout label appears Avoid: ✗ Red "Low Vol" warning during breakouts ✗ RVol < 1.0 at key levels ✗ Sustained volume not confirmed Signal Interpretation ⚡ Z>2 Labels - Statistically significant volume (95th+ percentile) - highest probability moves ↗️ OBV+ Labels - Bullish accumulation (OBV rising while price consolidates) ↘️ OBV- Labels - Bearish distribution (OBV falling while price rises) 🔵 Blue Background - Weekly volume elevated (confirms daily strength) ⚙️ Customization Basic Settings N Day Average - Number of historical days for comparison (default: 5) RVol Thresholds - Customize highlight levels (default: 1.2x, 1.5x) Visual Display Cap - Prevent extreme spikes from compressing view (default: 4.0x) Advanced Metrics (Toggle On/Off) Z-Score analysis Weekly RVol context OBV divergence detection Volume percentile ranking Breakout signal generation Table Customization Position - 9 placement options to avoid chart overlap Size - Tiny to Huge Colors - Full customization of positive/negative/neutral values Transparency - Adjustable background Debug Mode Enable Pine Logs for calculation transparency Adjustable log frequency Real-time calculation breakdown 🔬 Technical Details Algorithm: Binary search for historical lookups (O(log n) performance) Time-zone aware session detection DST-safe timestamp calculations Exponentially weighted standard deviation Anti-repainting architecture Performance: Optimized for max_bars_back = 5000 Efficient array management Built-in function optimization Memory-conscious data structures 📊 What Makes RVol+ Different? vs. Standard Volume: Context-aware (time-of-day matters) Statistical significance testing False breakout filtering vs. Basic RVol: Z-Score normalization (2-3 sigma detection) Multi-timeframe confirmation OBV divergence integration Sustained volume filtering Smart visual scaling vs. Professional Tools: Free and open-source Fully customizable No black-box algorithms Educational debug logs 💡 Best Practices Wait for Confirmation - Don't enter on first bar; wait for sustained volume ✓ Combine with Price Action - RVol validates, price structure determines entry Weekly Context Matters - Blue background = institutional interest Z-Score is King - Focus on ⚡ alerts for highest probability Avoid Low Volume Breakouts - Red ⚠️ labels = high failure risk 🎓 Trading Psychology Volume precedes price. When RVol+ shows: High RVol + Rising OBV = Accumulation before breakout High RVol at Resistance = Test of conviction Low RVol on Breakout = Retail-driven (fade candidate) Z-Score > 3 = Potential "whale" positioning 📝 Credits Based on the time-based RVol concept from /u/HurlTeaInTheSea, enhanced with: Statistical analysis (z-scores, percentiles) Multi-timeframe integration OBV divergence detection Professional-grade visualization Swing trading optimization 🔧 Version History v2.0 - Enhanced Edition Added Z-Score analysis Multi-timeframe volume context OBV divergence detection Breakout confirmation system Smart color coding Customizable stats table Debug logging mode Performance optimizations 📚 Learn More For optimal use with swing trading: Combine with support/resistance levels Watch for volume clusters in consolidation Use weekly timeframe for trend confirmation Monitor OBV divergence for early warnings ⚠️ Disclaimer This indicator is for educational purposes. Volume analysis is one component of trading decisions. Always use proper risk management, consider multiple timeframes, and validate signals with price structure. Past performance does not guarantee future results. 🚀 Getting Started Add indicator to chart Adjust "N Day Average" to your preference (5-10 days typical) Position stats table to avoid overlap Enable features you want to monitor Watch for 🚀 breakout confirmations! Happy Trading! 📈
Chỉ báo Pine Script®
của nippe678
[blackcat] L3 Improved Dual Ehlers BPF for Volatility DetectionOVERVIEW This script implements an advanced L3 Improved Dual Ehlers Bandpass Filter (BPF) for volatility detection, combining both L1 and L2 calculation methods to create a comprehensive trading signal. The script leverages John Ehlers' sophisticated digital signal processing techniques to identify market cycles and extract meaningful trading signals from price action. By combining multiple cycle detection methods and filtering approaches, it provides traders with a powerful tool for identifying trend changes, momentum shifts, and potential reversal points across various market conditions and timeframes. The L3 approach uniquely combines the outputs of both L1 (01 range) and L2 (-11 range) methods, creating a signal that ranges from -1~2 and provides enhanced sensitivity to market dynamics. FEATURES 🔄 Dual Calculation Methods: Choose between L1 (01 range), L2 (-11 range), or combine both for L3 signal (-1~2 range) to match your trading style 📊 Multiple Cycle Detection: Seven different dominant cycle calculation methods including HoDyDC (Hilbert Transform Dominant Cycle), PhAcDC (Phase Accumulation Dominant Cycle), DuDiDC (Duane Dominant Cycle), CycPer (Cycle Period), BPZC (Bandpass Zero Crossing), AutoPer (Autocorrelation Period), and DFTDC (Discrete Fourier Transform Dominant Cycle) 🎛️ Flexible Mixing Options: Six sophisticated mixing methods including weighted averaging, simple sum, difference extraction, dominant-only, subdominant-only, and adaptive mixing that adjusts based on signal strength 🌊 Bandpass Filtering: Precise bandwidth control for both dominant and subdominant filters, allowing fine-tuning of frequency response characteristics 📈 Advanced Divergence Detection: Robust algorithm for identifying bullish and bearish divergences with customizable lookback periods and range constraints 🎨 Comprehensive Visualization: Extensive customization options for all signals, colors, plot styles, and display elements 🔔 Comprehensive Alert System: Built-in alerts for divergence signals, zero line crosses, and various market conditions 📊 Real-time Cycle Information: Optional display of dominant and subdominant cycle periods for educational purposes 🔄 Adaptive Signal Processing: Dynamic adjustment of parameters based on market conditions and volatility 🎯 Multiple Signal Outputs: Simultaneous generation of L1, L2, and L3 signals for different trading strategies HOW TO USE Select Calculation Method: Choose between "l1" (01 range), "l2" (-11 range), or "both" (L3, -1~2 range) in the Calculation Method settings based on your preferred signal characteristics Configure Cycle Detection: Select your preferred Dominant Cycle Method from the seven available options and adjust the Cycle Part parameter (0.1-0.9) to fine-tune cycle sensitivity Set Subdominant Parameters: Configure the subdominant cycle either as a ratio of the dominant cycle or as a fixed period, depending on your analysis approach Adjust Filter Bandwidth: Fine-tune the bandwidth settings for both dominant and subdominant filters (0.1-1.0) to control the frequency response and signal smoothing Choose Mixing Method: Select how to combine the filters - weighted averaging for balance, sum for maximum sensitivity, difference for trend isolation, or adaptive mixing for dynamic response Configure Smoothing: Select from SMA, EMA, or HMA smoothing methods with adjustable length (1-20 bars) to reduce noise in the final signal Customize Visualization: Enable/disable individual plots, divergence detection, zero line, fill areas, and customize all colors to match your chart preferences Set Divergence Parameters: Configure lookback ranges (5-60 bars) for divergence detection to match your trading timeframe and style Monitor Signals: Watch for crosses above/below zero line and divergence patterns, paying attention to signal strength and consistency Set Up Alerts: Configure alerts for divergence signals, zero line crosses, and other market conditions to stay informed of trading opportunities LIMITATIONS The script requires the dc_ta library from blackcat1402 for several advanced cycle calculation methods (HoDyDC, PhAcDC, DuDiDC, CycPer, BPZC, AutoPer, DFTDC) L1 method operates in 01 range while L2 method uses -11 range, requiring different interpretation approaches Combined L3 signal ranges from -1~2 when both methods are selected, creating unique signal characteristics that traders must adapt to Divergence detection accuracy depends on proper lookback period settings and market volatility conditions Performance may be impacted with very long lookback ranges (>60 bars) or when multiple plots are simultaneously enabled The script is designed for non-overlay use and may not display correctly on certain chart types or with conflicting indicators Adaptive mixing method requires careful threshold tuning to avoid excessive signal fluctuation Cycle detection algorithms may produce unreliable results during low volatility or highly choppy market conditions The script assumes regular price data and may not perform optimally with irregular or gapped price sequences NOTES The script implements advanced mathematical calculations including bandpass filters, Hilbert transforms, and various cycle detection algorithms developed by John Ehlers For optimal results, experiment with different cycle detection methods and bandwidth settings across various market conditions and timeframes The adaptive mixing method automatically adjusts weights based on signal strength, providing dynamic response to changing market conditions Divergence detection works best when the "Plot Divergence" option is enabled and when combined with other technical analysis tools Zero line crosses can indicate potential trend changes or momentum shifts, especially when confirmed by volume or other indicators The script includes commented code for cycle information display that can be enabled if you want to monitor cycle periods in real-time Different calculation methods may perform better in different market environments - L1 tends to be smoother while L2 is more sensitive The subdominant cycle helps filter out noise and provides additional confirmation for signals generated by the dominant cycle Bandwidth settings control the filter's frequency response - lower values provide more smoothing while higher values increase sensitivity Mixing methods offer different approaches to combining signals - weighted averaging is generally most reliable for most trading applications THANKS Special thanks to John Ehlers for his pioneering work in cycle analysis and digital signal processing for financial markets. This script implements and significantly improves upon his bandpass filter methodology, incorporating multiple advanced techniques from his extensive body of work. Also heartfelt thanks to blackcat1402 for the dc_ta library that provides essential cycle calculation methods and for maintaining such a valuable resource for the Pine Script community. Additional appreciation to the TradingView platform for providing the tools and environment that make sophisticated technical analysis accessible to traders worldwide. This script represents a collaborative effort in advancing the field of algorithmic trading and technical analysis.
Chỉ báo Pine Script®
của blackcat1402
Langlands-Operadic Möbius Vortex (LOMV)Langlands-Operadic Möbius Vortex (LOMV) Where Pure Mathematics Meets Market Reality A Revolutionary Synthesis of Number Theory, Category Theory, and Market Dynamics 🎓 THEORETICAL FOUNDATION The Langlands-Operadic Möbius Vortex represents a groundbreaking fusion of three profound mathematical frameworks that have never before been combined for market analysis: The Langlands Program: Harmonic Analysis in Markets Developed by Robert Langlands (Fields Medal recipient), the Langlands Program creates bridges between number theory, algebraic geometry, and harmonic analysis. In our indicator: L-Function Implementation: - Utilizes the Möbius function μ(n) for weighted price analysis - Applies Riemann zeta function convergence principles - Calculates quantum harmonic resonance between -2 and +2 - Measures deep mathematical patterns invisible to traditional analysis The L-Function core calculation employs: L_sum = Σ(return_val × μ(n) × n^(-s)) Where s is the critical strip parameter (0.5-2.5), controlling mathematical precision and signal smoothness. Operadic Composition Theory: Multi-Strategy Democracy Category theory and operads provide the mathematical framework for composing multiple trading strategies into a unified signal. This isn't simple averaging - it's mathematical composition using: Strategy Composition Arity (2-5 strategies): - Momentum analysis via RSI transformation - Mean reversion through Bollinger Band mathematics - Order Flow Polarity Index (revolutionary T3-smoothed volume analysis) - Trend detection using Directional Movement - Higher timeframe momentum confirmation Agreement Threshold System: Democratic voting where strategies must reach consensus before signal generation. This prevents false signals during market uncertainty. Möbius Function: Number Theory in Action The Möbius function μ(n) forms the mathematical backbone: - μ(n) = 1 if n is a square-free positive integer with even number of prime factors - μ(n) = -1 if n is a square-free positive integer with odd number of prime factors - μ(n) = 0 if n has a squared prime factor This creates oscillating weights that reveal hidden market periodicities and harmonic structures. 🔧 COMPREHENSIVE INPUT SYSTEM Langlands Program Parameters Modular Level N (5-50, default 30): Primary lookback for quantum harmonic analysis. Optimized by timeframe: - Scalping (1-5min): 15-25 - Day Trading (15min-1H): 25-35 - Swing Trading (4H-1D): 35-50 - Asset-specific: Crypto 15-25, Stocks 30-40, Forex 35-45 L-Function Critical Strip (0.5-2.5, default 1.5): Controls Riemann zeta convergence precision: - Higher values: More stable, smoother signals - Lower values: More reactive, catches quick moves - High frequency: 0.8-1.2, Medium: 1.3-1.7, Low: 1.8-2.3 Frobenius Trace Period (5-50, default 21): Galois representation lookback for price-volume correlation: - Measures harmonic relationships in market flows - Scalping: 8-15, Day Trading: 18-25, Swing: 25-40 HTF Multi-Scale Analysis: Higher timeframe context prevents trading against major trends: - Provides market bias and filters signals - Improves win rates by 15-25% through trend alignment Operadic Composition Parameters Strategy Composition Arity (2-5, default 4): Number of algorithms composed for final signal: - Conservative: 4-5 strategies (higher confidence) - Moderate: 3-4 strategies (balanced approach) - Aggressive: 2-3 strategies (more frequent signals) Category Agreement Threshold (2-5, default 3): Democratic voting minimum for signal generation: - Higher agreement: Fewer but higher quality signals - Lower agreement: More signals, potential false positives Swiss-Cheese Mixing (0.1-0.5, default 0.382): Golden ratio φ⁻¹ based blending of trend factors: - 0.382 is φ⁻¹, optimal for natural market fractals - Higher values: Stronger trend following - Lower values: More contrarian signals OFPI Configuration: - OFPI Length (5-30, default 14): Order Flow calculation period - T3 Smoothing (3-10, default 5): Advanced exponential smoothing - T3 Volume Factor (0.5-1.0, default 0.7): Smoothing aggressiveness control Unified Scoring System Component Weights (sum ≈ 1.0): - L-Function Weight (0.1-0.5, default 0.3): Mathematical harmony emphasis - Galois Rank Weight (0.1-0.5, default 0.2): Market structure complexity - Operadic Weight (0.1-0.5, default 0.3): Multi-strategy consensus - Correspondence Weight (0.1-0.5, default 0.2): Theory-practice alignment Signal Threshold (0.5-10.0, default 5.0): Quality filter producing: - 8.0+: EXCEPTIONAL signals only - 6.0-7.9: STRONG signals - 4.0-5.9: MODERATE signals - 2.0-3.9: WEAK signals 🎨 ADVANCED VISUAL SYSTEM Multi-Dimensional Quantum Aura Bands Five-layer resonance field showing market energy: - Colors: Theme-matched gradients (Quantum purple, Holographic cyan, etc.) - Expansion: Dynamic based on score intensity and volatility - Function: Multi-timeframe support/resistance zones Morphism Flow Portals Category theory visualization showing market topology: - Green/Cyan Portals: Bullish mathematical flow - Red/Orange Portals: Bearish mathematical flow - Size/Intensity: Proportional to signal strength - Recursion Depth (1-8): Nested patterns for flow evolution Fractal Grid System Dynamic support/resistance with projected L-Scores: - Multiple Timeframes: 10, 20, 30, 40, 50-period highs/lows - Smart Spacing: Prevents level overlap using ATR-based minimum distance - Projections: Estimated signal scores when price reaches levels - Usage: Precise entry/exit timing with mathematical confirmation Wick Pressure Analysis Rejection level prediction using candle mathematics: - Upper Wicks: Selling pressure zones (purple/red lines) - Lower Wicks: Buying pressure zones (purple/green lines) - Glow Intensity (1-8): Visual emphasis and line reach - Application: Confluence with fractal grid creates high-probability zones Regime Intensity Heatmap Background coloring showing market energy: - Black/Dark: Low activity, range-bound markets - Purple Glow: Building momentum and trend development - Bright Purple: High activity, strong directional moves - Calculation: Combines trend, momentum, volatility, and score intensity Six Professional Themes - Quantum: Purple/violet for general trading and mathematical focus - Holographic: Cyan/magenta optimized for cryptocurrency markets - Crystalline: Blue/turquoise for conservative, stability-focused trading - Plasma: Gold/magenta for high-energy volatility trading - Cosmic Neon: Bright neon colors for maximum visibility and aggressive trading 📊 INSTITUTIONAL-GRADE DASHBOARD Unified AI Score Section - Total Score (-10 to +10): Primary decision metric - >5: Strong bullish signals - <-5: Strong bearish signals - Quality ratings: EXCEPTIONAL > STRONG > MODERATE > WEAK - Component Analysis: Individual L-Function, Galois, Operadic, and Correspondence contributions Order Flow Analysis Revolutionary OFPI integration: - OFPI Value (-100% to +100%): Real buying vs selling pressure - Visual Gauge: Horizontal bar chart showing flow intensity - Momentum Status: SHIFTING, ACCELERATING, STRONG, MODERATE, or WEAK - Trading Application: Flow shifts often precede major moves Signal Performance Tracking - Win Rate Monitoring: Real-time success percentage with emoji indicators - Signal Count: Total signals generated for frequency analysis - Current Position: LONG, SHORT, or NONE with P&L tracking - Volatility Regime: HIGH, MEDIUM, or LOW classification Market Structure Analysis - Möbius Field Strength: Mathematical field oscillation intensity - CHAOTIC: High complexity, use wider stops - STRONG: Active field, normal position sizing - MODERATE: Balanced conditions - WEAK: Low activity, consider smaller positions - HTF Trend: Higher timeframe bias (BULL/BEAR/NEUTRAL) - Strategy Agreement: Multi-algorithm consensus level Position Management When in trades, displays: - Entry Price: Original signal price - Current P&L: Real-time percentage with risk level assessment - Duration: Bars in trade for timing analysis - Risk Level: HIGH/MEDIUM/LOW based on current exposure 🚀 SIGNAL GENERATION LOGIC Balanced Long/Short Architecture The indicator generates signals through multiple convergent pathways: Long Entry Conditions: - Score threshold breach with algorithmic agreement - Strong bullish order flow (OFPI > 0.15) with positive composite signal - Bullish pattern recognition with mathematical confirmation - HTF trend alignment with momentum shifting - Extreme bullish OFPI (>0.3) with any positive score Short Entry Conditions: - Score threshold breach with bearish agreement - Strong bearish order flow (OFPI < -0.15) with negative composite signal - Bearish pattern recognition with mathematical confirmation - HTF trend alignment with momentum shifting - Extreme bearish OFPI (<-0.3) with any negative score Exit Logic: - Score deterioration below continuation threshold - Signal quality degradation - Opposing order flow acceleration - 10-bar minimum between signals prevents overtrading ⚙️ OPTIMIZATION GUIDELINES Asset-Specific Settings Cryptocurrency Trading: - Modular Level: 15-25 (capture volatility) - L-Function Precision: 0.8-1.3 (reactive to price swings) - OFPI Length: 10-20 (fast correlation shifts) - Cascade Levels: 5-7, Theme: Holographic Stock Index Trading: - Modular Level: 25-35 (balanced trending) - L-Function Precision: 1.5-1.8 (stable patterns) - OFPI Length: 14-20 (standard correlation) - Cascade Levels: 4-5, Theme: Quantum Forex Trading: - Modular Level: 35-45 (smooth trends) - L-Function Precision: 1.6-2.1 (high smoothing) - OFPI Length: 18-25 (disable volume amplification) - Cascade Levels: 3-4, Theme: Crystalline Timeframe Optimization Scalping (1-5 minute charts): - Reduce all lookback parameters by 30-40% - Increase L-Function precision for noise reduction - Enable all visual elements for maximum information - Use Small dashboard to save screen space Day Trading (15 minute - 1 hour): - Use default parameters as starting point - Adjust based on market volatility - Normal dashboard provides optimal information density - Focus on OFPI momentum shifts for entries Swing Trading (4 hour - Daily): - Increase lookback parameters by 30-50% - Higher L-Function precision for stability - Large dashboard for comprehensive analysis - Emphasize HTF trend alignment 🏆 ADVANCED TRADING STRATEGIES The Mathematical Confluence Method 1. Wait for Fractal Grid level approach 2. Confirm with projected L-Score > threshold 3. Verify OFPI alignment with direction 4. Enter on portal signal with quality ≥ STRONG 5. Exit on score deterioration or opposing flow The Regime Trading System 1. Monitor Aether Flow background intensity 2. Trade aggressively during bright purple periods 3. Reduce position size during dark periods 4. Use Möbius Field strength for stop placement 5. Align with HTF trend for maximum probability The OFPI Momentum Strategy 1. Watch for momentum shifting detection 2. Confirm with accelerating flow in direction 3. Enter on immediate portal signal 4. Scale out at Fibonacci levels 5. Exit on flow deceleration or reversal ⚠️ RISK MANAGEMENT INTEGRATION Mathematical Position Sizing - Use Galois Rank for volatility-adjusted sizing - Möbius Field strength determines stop width - Fractal Dimension guides maximum exposure - OFPI momentum affects entry timing Signal Quality Filtering - Trade only STRONG or EXCEPTIONAL quality signals - Increase position size with higher agreement levels - Reduce risk during CHAOTIC Möbius field periods - Respect HTF trend alignment for directional bias 🔬 DEVELOPMENT JOURNEY Creating the LOMV was an extraordinary mathematical undertaking that pushed the boundaries of what's possible in technical analysis. This indicator almost didn't happen. The theoretical complexity nearly proved insurmountable. The Mathematical Challenge Implementing the Langlands Program required deep research into: - Number theory and the Möbius function - Riemann zeta function convergence properties - L-function analytical continuation - Galois representations in finite fields The mathematical literature spans decades of pure mathematics research, requiring translation from abstract theory to practical market application. The Computational Complexity Operadic composition theory demanded: - Category theory implementation in Pine Script - Multi-dimensional array management for strategy composition - Real-time democratic voting algorithms - Performance optimization for complex calculations The Integration Breakthrough Bringing together three disparate mathematical frameworks required: - Novel approaches to signal weighting and combination - Revolutionary Order Flow Polarity Index development - Advanced T3 smoothing implementation - Balanced signal generation preventing directional bias Months of intensive research culminated in breakthrough moments when the mathematics finally aligned with market reality. The result is an indicator that reveals market structure invisible to conventional analysis while maintaining practical trading utility. 🎯 PRACTICAL IMPLEMENTATION Getting Started 1. Apply indicator with default settings 2. Select appropriate theme for your markets 3. Observe dashboard metrics during different market conditions 4. Practice signal identification without trading 5. Gradually adjust parameters based on observations Signal Confirmation Process - Never trade on score alone - verify quality rating - Confirm OFPI alignment with intended direction - Check fractal grid level proximity for timing - Ensure Möbius field strength supports position size - Validate against HTF trend for bias confirmation Performance Monitoring - Track win rate in dashboard for strategy assessment - Monitor component contributions for optimization - Adjust threshold based on desired signal frequency - Document performance across different market regimes 🌟 UNIQUE INNOVATIONS 1. First Integration of Langlands Program mathematics with practical trading 2. Revolutionary OFPI with T3 smoothing and momentum detection 3. Operadic Composition using category theory for signal democracy 4. Dynamic Fractal Grid with projected L-Score calculations 5. Multi-Dimensional Visualization through morphism flow portals 6. Regime-Adaptive Background showing market energy intensity 7. Balanced Signal Generation preventing directional bias 8. Professional Dashboard with institutional-grade metrics 📚 EDUCATIONAL VALUE The LOMV serves as both a practical trading tool and an educational gateway to advanced mathematics. Traders gain exposure to: - Pure mathematics applications in markets - Category theory and operadic composition - Number theory through Möbius function implementation - Harmonic analysis via L-function calculations - Advanced signal processing through T3 smoothing ⚖️ RESPONSIBLE USAGE This indicator represents advanced mathematical research applied to market analysis. While the underlying mathematics are rigorously implemented, markets remain inherently unpredictable. Key Principles: - Use as part of comprehensive trading strategy - Implement proper risk management at all times - Backtest thoroughly before live implementation - Understand that past performance does not guarantee future results - Never risk more than you can afford to lose The mathematics reveal deep market structure, but successful trading requires discipline, patience, and sound risk management beyond any indicator. 🔮 CONCLUSION The Langlands-Operadic Möbius Vortex represents a quantum leap forward in technical analysis, bringing PhD-level pure mathematics to practical trading while maintaining visual elegance and usability. From the harmonic analysis of the Langlands Program to the democratic composition of operadic theory, from the number-theoretic precision of the Möbius function to the revolutionary Order Flow Polarity Index, every component works in mathematical harmony to reveal the hidden order within market chaos. This is more than an indicator - it's a mathematical lens that transforms how you see and understand market structure. Trade with mathematical precision. Trade with the LOMV. *"Mathematics is the language with which God has written the universe." - Galileo Galilei* *In markets, as in nature, profound mathematical beauty underlies apparent chaos. The LOMV reveals this hidden order.* — Dskyz, Trade with insight. Trade with anticipation.
Chỉ báo Pine Script®
của DskyzInvestments
29
MLExtensions_CoreLibrary "MLExtensions_Core" A set of extension methods for a novel implementation of a Approximate Nearest Neighbors (ANN) algorithm in Lorentzian space, focused on computation. normalizeDeriv(src, quadraticMeanLength)   Returns the smoothed hyperbolic tangent of the input series.   Parameters:      src (float) : The input series (i.e., the first-order derivative for price).      quadraticMeanLength (int) : The length of the quadratic mean (RMS).   Returns: nDeriv The normalized derivative of the input series. normalize(src, min, max)   Rescales a source value with an unbounded range to a target range.   Parameters:      src (float) : The input series      min (float) : The minimum value of the unbounded range      max (float) : The maximum value of the unbounded range   Returns: The normalized series rescale(src, oldMin, oldMax, newMin, newMax)   Rescales a source value with a bounded range to anther bounded range   Parameters:      src (float) : The input series      oldMin (float) : The minimum value of the range to rescale from      oldMax (float) : The maximum value of the range to rescale from      newMin (float) : The minimum value of the range to rescale to      newMax (float) : The maximum value of the range to rescale to   Returns: The rescaled series getColorShades(color)   Creates an array of colors with varying shades of the input color   Parameters:      color (color) : The color to create shades of   Returns: An array of colors with varying shades of the input color getPredictionColor(prediction, neighborsCount, shadesArr)   Determines the color shade based on prediction percentile   Parameters:      prediction (float) : Value of the prediction      neighborsCount (int) : The number of neighbors used in a nearest neighbors classification      shadesArr (array) : An array of colors with varying shades of the input color   Returns: shade Color shade based on prediction percentile color_green(prediction)   Assigns varying shades of the color green based on the KNN classification   Parameters:      prediction (float) : Value (int|float) of the prediction   Returns: color color_red(prediction)   Assigns varying shades of the color red based on the KNN classification   Parameters:      prediction (float) : Value of the prediction   Returns: color tanh(src)   Returns the the hyperbolic tangent of the input series. The sigmoid-like hyperbolic tangent function is used to compress the input to a value between -1 and 1.   Parameters:      src (float) : The input series (i.e., the normalized derivative).   Returns: tanh The hyperbolic tangent of the input series. dualPoleFilter(src, lookback)   Returns the smoothed hyperbolic tangent of the input series.   Parameters:      src (float) : The input series (i.e., the hyperbolic tangent).      lookback (int) : The lookback window for the smoothing.   Returns: filter The smoothed hyperbolic tangent of the input series. tanhTransform(src, smoothingFrequency, quadraticMeanLength)   Returns the tanh transform of the input series.   Parameters:      src (float) : The input series (i.e., the result of the tanh calculation).      smoothingFrequency (int)      quadraticMeanLength (int)   Returns: signal The smoothed hyperbolic tangent transform of the input series. n_rsi(src, n1, n2)   Returns the normalized RSI ideal for use in ML algorithms.   Parameters:      src (float) : The input series (i.e., the result of the RSI calculation).      n1 (simple int) : The length of the RSI.      n2 (simple int) : The smoothing length of the RSI.   Returns: signal The normalized RSI. n_cci(src, n1, n2)   Returns the normalized CCI ideal for use in ML algorithms.   Parameters:      src (float) : The input series (i.e., the result of the CCI calculation).      n1 (simple int) : The length of the CCI.      n2 (simple int) : The smoothing length of the CCI.   Returns: signal The normalized CCI. n_wt(src, n1, n2)   Returns the normalized WaveTrend Classic series ideal for use in ML algorithms.   Parameters:      src (float) : The input series (i.e., the result of the WaveTrend Classic calculation).      n1 (simple int)      n2 (simple int)   Returns: signal The normalized WaveTrend Classic series. n_adx(highSrc, lowSrc, closeSrc, n1)   Returns the normalized ADX ideal for use in ML algorithms.   Parameters:      highSrc (float) : The input series for the high price.      lowSrc (float) : The input series for the low price.      closeSrc (float) : The input series for the close price.      n1 (simple int) : The length of the ADX. regime_filter(src, threshold, useRegimeFilter)   Parameters:      src (float)      threshold (float)      useRegimeFilter (bool) filter_adx(src, length, adxThreshold, useAdxFilter)   filter_adx   Parameters:      src (float) : The source series.      length (simple int) : The length of the ADX.      adxThreshold (int) : The ADX threshold.      useAdxFilter (bool) : Whether to use the ADX filter.   Returns: The ADX. filter_volatility(minLength, maxLength, sensitivityMultiplier, useVolatilityFilter)   filter_volatility   Parameters:      minLength (simple int) : The minimum length of the ATR.      maxLength (simple int) : The maximum length of the ATR.      sensitivityMultiplier (float) : Multiplier for the historical ATR to control sensitivity.      useVolatilityFilter (bool) : Whether to use the volatility filter.   Returns: Boolean indicating whether or not to let the signal pass through the filter.
Thư viện Pine Script®
của viorel8
Volume Predictor [PhenLabs]📊 Volume Predictor Version: PineScript™ v6 📌 Description The Volume Predictor is an advanced technical indicator that leverages machine learning and statistical modeling techniques to forecast future trading volume. This innovative tool analyzes historical volume patterns to predict volume levels for upcoming bars, providing traders with valuable insights into potential market activity. By combining multiple prediction algorithms with pattern recognition techniques, the indicator delivers forward-looking volume projections that can enhance trading strategies and market analysis. 🚀 Points of Innovation: Machine learning pattern recognition using Lorentzian distance metrics Multi-algorithm prediction framework with algorithm selection Ensemble learning approach combining multiple prediction methods Real-time accuracy metrics with visual performance dashboard Dynamic volume normalization for consistent scale representation Forward-looking visualization with configurable prediction horizon 🔧 Core Components Pattern Recognition Engine : Identifies similar historical volume patterns using Lorentzian distance metrics Multi-Algorithm Framework : Offers five distinct prediction methods with configurable parameters Volume Normalization : Converts raw volume to percentage scale for consistent analysis Accuracy Tracking : Continuously evaluates prediction performance against actual outcomes Advanced Visualization : Displays actual vs. predicted volume with configurable future bar projections Interactive Dashboard : Shows real-time performance metrics and prediction accuracy 🔥 Key Features The indicator provides comprehensive volume analysis through: Multiple Prediction Methods : Choose from Lorentzian, KNN Pattern, Ensemble, EMA, or Linear Regression algorithms Pattern Matching : Identifies similar historical volume patterns to project future volume Adaptive Predictions : Generates volume forecasts for multiple bars into the future Performance Tracking : Calculates and displays real-time prediction accuracy metrics Normalized Scale : Presents volume as a percentage of historical maximums for consistent analysis Customizable Visualization : Configure how predictions and actual volumes are displayed Interactive Dashboard : View algorithm performance metrics in a customizable information panel 🎨 Visualization Actual Volume Columns : Color-coded green/red bars showing current normalized volume Prediction Columns : Semi-transparent blue columns representing predicted volume levels Future Bar Projections : Forward-looking volume predictions with configurable transparency Prediction Dots : Optional white dots highlighting future prediction points Reference Lines : Visual guides showing the normalized volume scale Performance Dashboard : Customizable panel displaying prediction method and accuracy metrics 📖 Usage Guidelines History Lookback Period Default: 20 Range: 5-100 This setting determines how many historical bars are analyzed for pattern matching. A longer period provides more historical data for pattern recognition but may reduce responsiveness to recent changes. A shorter period emphasizes recent market behavior but might miss longer-term patterns. 🧠 Prediction Method Algorithm Default: Lorentzian Options: Lorentzian, KNN Pattern, Ensemble, EMA, Linear Regression Selects the algorithm used for volume prediction: Lorentzian: Uses Lorentzian distance metrics for pattern recognition, offering excellent noise resistance KNN Pattern: Traditional K-Nearest Neighbors approach for historical pattern matching Ensemble: Combines multiple methods with weighted averaging for robust predictions EMA: Simple exponential moving average projection for trend-following predictions Linear Regression: Projects future values based on linear trend analysis Pattern Length Default: 5 Range: 3-10 Defines the number of bars in each pattern for machine learning methods. Shorter patterns increase sensitivity to recent changes, while longer patterns may identify more complex structures but require more historical data. Neighbors Count Default: 3 Range: 1-5 Sets the K value (number of nearest neighbors) used in KNN and Lorentzian methods. Higher values produce smoother predictions by averaging more historical patterns, while lower values may capture more specific patterns but could be more susceptible to noise. Prediction Horizon Default: 5 Range: 1-10 Determines how many future bars to predict. Longer horizons provide more forward-looking information but typically decrease accuracy as the prediction window extends. 📊 Display Settings Display Mode Default: Overlay Options: Overlay, Prediction Only Controls how volume information is displayed: Overlay: Shows both actual volume and predictions on the same chart Prediction Only: Displays only the predictions without actual volume Show Prediction Dots Default: false When enabled, adds white dots to future predictions for improved visibility and clarity. Future Bar Transparency (%) Default: 70 Range: 0-90 Controls the transparency of future prediction bars. Higher values make future bars more transparent, while lower values make them more visible. 📱 Dashboard Settings Show Dashboard Default: true Toggles display of the prediction accuracy dashboard. When enabled, shows real-time accuracy metrics. Dashboard Location Default: Bottom Right Options: Top Left, Top Right, Bottom Left, Bottom Right Determines where the dashboard appears on the chart. Dashboard Text Size Default: Normal Options: Small, Normal, Large Controls the size of text in the dashboard for various display sizes. Dashboard Style Default: Solid Options: Solid, Transparent Sets the visual style of the dashboard background. Understanding Accuracy Metrics The dashboard provides key performance metrics to evaluate prediction quality: Average Error Shows the average difference between predicted and actual values Positive values indicate the prediction tends to be higher than actual volume Negative values indicate the prediction tends to be lower than actual volume Values closer to zero indicate better prediction accuracy Accuracy Percentage A measure of how close predictions are to actual outcomes Higher percentages (>70%) indicate excellent prediction quality Moderate percentages (50-70%) indicate acceptable predictions Lower percentages (<50%) suggest weaker prediction reliability The accuracy metrics are color-coded for quick assessment: Green: Strong prediction performance Orange: Moderate prediction performance Red: Weaker prediction performance ✅ Best Use Cases Anticipate upcoming volume spikes or drops Identify potential volume divergences from price action Plan entries and exits around expected volume changes Filter trading signals based on predicted volume support Optimize position sizing by forecasting market participation Prepare for potential volatility changes signaled by volume predictions Enhance technical pattern analysis with volume projection context ⚠️ Limitations Volume predictions become less accurate over longer time horizons Performance varies based on market conditions and asset characteristics Works best on liquid assets with consistent volume patterns Requires sufficient historical data for pattern recognition Sudden market events can disrupt prediction accuracy Volume spikes may be muted in predictions due to normalization 💡 What Makes This Unique Machine Learning Approach : Applies Lorentzian distance metrics for robust pattern matching Algorithm Selection : Offers multiple prediction methods to suit different market conditions Real-time Accuracy Tracking : Provides continuous feedback on prediction performance Forward Projection : Visualizes multiple future bars with configurable display options Normalized Scale : Presents volume as a percentage of maximum volume for consistent analysis Interactive Dashboard : Displays key metrics with customizable appearance and placement 🔬 How It Works The Volume Predictor processes market data through five main steps: 1. Volume Normalization: Converts raw volume to percentage of maximum volume in lookback period Creates consistent scale representation across different timeframes and assets Stores historical normalized volumes for pattern analysis 2. Pattern Detection: Identifies similar volume patterns in historical data Uses Lorentzian distance metrics for robust similarity measurement Determines strength of pattern match for prediction weighting 3. Algorithm Processing: Applies selected prediction algorithm to historical patterns For KNN/Lorentzian: Finds K nearest neighbors and calculates weighted prediction For Ensemble: Combines multiple methods with optimized weighting For EMA/Linear Regression: Projects trends based on statistical models 4. Accuracy Calculation: Compares previous predictions to actual outcomes Calculates average error and prediction accuracy Updates performance metrics in real-time 5. Visualization: Displays normalized actual volume with color-coding Shows current and future volume predictions Presents performance metrics through interactive dashboard 💡 Note: The Volume Predictor performs optimally on liquid assets with established volume patterns. It’s most effective when used in conjunction with price action analysis and other technical indicators. The multi-algorithm approach allows adaptation to different market conditions by switching prediction methods. Pay special attention to the accuracy metrics when evaluating prediction reliability, as sudden market changes can temporarily reduce prediction quality. The normalized percentage scale makes the indicator consistent across different assets and timeframes, providing a standardized approach to volume analysis.
Chỉ báo Pine Script®
của PhenLabs
2
Adaptive Fisherized Z-scoreHello Fellas, It's time for a new adaptive fisherized indicator of me, where I apply adaptive length and more on a classic indicator. Today, I chose the Z-score, also called standard score, as indicator of interest. Special Features Advanced Smoothing: JMA, T3, Hann Window and Super Smoother Adaptive Length Algorithms: In-Phase Quadrature, Homodyne Discriminator, Median and Hilbert Transform Inverse Fisher Transform (IFT) Signals: Enter Long, Enter Short, Exit Long and Exit Short Bar Coloring: Presents the trade state as bar colors Band Levels: Changes the band levels Decision Making When you create such a mod you need to think about which concepts are the best to conclude. I decided to take Inverse Fisher Transform instead of normalization to make a version which fits to a fixed scale to avoid the usual distortion created by normalization. Moreover, I chose JMA, T3, Hann Window and Super Smoother, because JMA and T3 are the bleeding-edge MA's at the moment with the best balance of lag and responsiveness. Additionally, I chose Hann Window and Super Smoother because of their extraordinary smoothing capabilities and because Ehlers favours them. Furthermore, I decided to choose the half length of the dominant cycle instead of the full dominant cycle to make the indicator more responsive which is very important for a signal emitter like Z-score. Signal emitters always need to be faster or have the same speed as the filters they are combined with. Usage The Z-score is a low timeframe scalper which works best during choppy/ranging phases. The direction you should trade is determined by the last trend change. E.g. when the last trend change was from bearish market to bullish market and you are now in a choppy/ranging phase confirmed by e.g. Chop Zone or KAMA slope you want to do long trades. Interpretation The Z-score indicator is a momentum indicator which shows the number of standard deviations by which the value of a raw score (price/source) is above or below the mean value of what is being observed or measured. Easily explained, it is almost the same as Bollinger Bands with another visual representation form. Signals B -> Buy -> Z-score crosses above lower band S -> Short -> Z-score crosses below upper band BE -> Buy Exit -> Z-score crosses above 0 SE -> Sell Exit -> Z-score crosses below 0 If you were reading till here, thank you already. Now, follows a bunch of knowledge for people who don't know the concepts I talk about. T3 The T3 moving average, short for "Tim Tillson's Triple Exponential Moving Average," is a technical indicator used in financial markets and technical analysis to smooth out price data over a specific period. It was developed by Tim Tillson, a software project manager at Hewlett-Packard, with expertise in Mathematics and Computer Science. The T3 moving average is an enhancement of the traditional Exponential Moving Average (EMA) and aims to overcome some of its limitations. The primary goal of the T3 moving average is to provide a smoother representation of price trends while minimizing lag compared to other moving averages like Simple Moving Average (SMA), Weighted Moving Average (WMA), or EMA. To compute the T3 moving average, it involves a triple smoothing process using exponential moving averages. Here's how it works: Calculate the first exponential moving average (EMA1) of the price data over a specific period 'n.' Calculate the second exponential moving average (EMA2) of EMA1 using the same period 'n.' Calculate the third exponential moving average (EMA3) of EMA2 using the same period 'n.' The formula for the T3 moving average is as follows: T3 = 3 * (EMA1) - 3 * (EMA2) + (EMA3) By applying this triple smoothing process, the T3 moving average is intended to offer reduced noise and improved responsiveness to price trends. It achieves this by incorporating multiple time frames of the exponential moving averages, resulting in a more accurate representation of the underlying price action. JMA The Jurik Moving Average (JMA) is a technical indicator used in trading to predict price direction. Developed by Mark Jurik, it’s a type of weighted moving average that gives more weight to recent market data rather than past historical data. JMA is known for its superior noise elimination. It’s a causal, nonlinear, and adaptive filter, meaning it responds to changes in price action without introducing unnecessary lag. This makes JMA a world-class moving average that tracks and smooths price charts or any market-related time series with surprising agility. In comparison to other moving averages, such as the Exponential Moving Average (EMA), JMA is known to track fast price movement more accurately. This allows traders to apply their strategies to a more accurate picture of price action. Inverse Fisher Transform The Inverse Fisher Transform is a transform used in DSP to alter the Probability Distribution Function (PDF) of a signal or in our case of indicators. The result of using the Inverse Fisher Transform is that the output has a very high probability of being either +1 or –1. This bipolar probability distribution makes the Inverse Fisher Transform ideal for generating an indicator that provides clear buy and sell signals. Hann Window The Hann function (aka Hann Window) is named after the Austrian meteorologist Julius von Hann. It is a window function used to perform Hann smoothing. Super Smoother The Super Smoother uses a special mathematical process for the smoothing of data points. The Super Smoother is a technical analysis indicator designed to be smoother and with less lag than a traditional moving average. Adaptive Length Length based on the dominant cycle length measured by a "dominant cycle measurement" algorithm. Happy Trading! Best regards, simwai --- Credits to @cheatcountry @everget @loxx @DasanC @blackcat1402
Chỉ báo Pine Script®
của simwai
4
Channel Based Zigzag [HeWhoMustNotBeNamed]🎲 Concept Zigzag is built based on the price and number of offset bars. But, in this experiment, we build zigzag based on different bands such as Bollinger Band, Keltner Channel and Donchian Channel. The process is simple: 🎯 Derive bands based on input parameters 🎯 High of a bar is considered as pivot high only if the high price is above or equal to upper band. 🎯 Similarly low of a bar is considered as pivot low only if low price is below or equal to lower band. 🎯 Adding the pivot high/low follows same logic as that of regular zigzag where pivot high is always followed by pivot low and vice versa. 🎯 If the new pivot added is of same direction as that of last pivot, then both pivots are compared with each other and only the extreme one is kept. (Highest in case of pivot high and lowest in case of pivot low) 🎯 If a bar has both pivot high and pivot low - pivot with same direction as previous pivot is added to the list first before adding the pivot with opposite direction. 🎲 Use Cases Can be used for pattern recognition algorithms instead of standard zigzag. This will help derive patterns which are relative to bands and channels. Example: John Bollinger explains how to manually scan double tap using Bollinger Bands in this video: www.youtube.com This modified zigzag base can be used to achieve the same using algorithmic means. 🎲 Settings Few simple configurations which will let you select the band properties. Notice that there is no zigzag length here. All the calculations depend on the bands. With bands display, indicator looks something like this Note that pivots do not always represent highest/lowest prices. They represent highest/lowest price relative to bands. As mentioned many times, application of zigzag is not for buying at lower price and selling at higher price. It is mainly used for pattern recognition either manually or via algorithms. Lets build new Harmonic, Chart patterns, Trend Lines using the new zigzag?
Chỉ báo Pine Script®
của Trendoscope
18
cbndLibrary "cbnd" Description: A standalone Cumulative Bivariate Normal Distribution (CBND) functions that do not require any external libraries. This includes 3 different CBND calculations: Drezner(1978), Drezner and Wesolowsky (1990), and Genz (2004) Comments: The standardized cumulative normal distribution function returns the probability that one random variable is less than a and that a second random variable is less than b when the correlation between the two variables is p. Since no closed-form solution exists for the bivariate cumulative normal distribution, we present three approximations. The first one is the well-known Drezner (1978) algorithm. The second one is the more efficient Drezner and Wesolowsky (1990) algorithm. The third is the Genz (2004) algorithm, which is the most accurate one and therefore our recommended algorithm. West (2005b) and Agca and Chance (2003) discuss the speed and accuracy of bivariate normal distribution approximations for use in option pricing in ore detail. Reference: The Complete Guide to Option Pricing Formulas, 2nd ed. (Espen Gaarder Haug) CBND1(A, b, rho)   Returns the Cumulative Bivariate Normal Distribution (CBND) using Drezner 1978 Algorithm   Parameters:      A : float,      b : float,      rho : float,   Returns: float. CBND2(A, b, rho)   Returns the Cumulative Bivariate Normal Distribution (CBND) using Drezner and Wesolowsky (1990) function   Parameters:      A : float,      b : float,      rho : float,   Returns: float. CBND3(x, y, rho)   Returns the Cumulative Bivariate Normal Distribution (CBND) using Genz (2004) algorithm (this is the preferred method)   Parameters:      x : float,      y : float,      rho : float,   Returns: float.
Thư viện Pine Script®
của loxx
STD-Stepped Fast Cosine Transform Moving Average [Loxx]STD-Stepped Fast Cosine Transform Moving Average is an experimental moving average that uses Fast Cosine Transform to calculate a moving average. This indicator has standard deviation stepping in order to smooth the trend by weeding out low volatility movements. What is the Discrete Cosine Transform? A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression. It is used in most digital media, including digital images (such as JPEG and HEIF, where small high-frequency components can be discarded), digital video (such as MPEG and H.26x), digital audio (such as Dolby Digital, MP3 and AAC), digital television (such as SDTV, HDTV and VOD), digital radio (such as AAC+ and DAB+), and speech coding (such as AAC-LD, Siren and Opus). DCTs are also important to numerous other applications in science and engineering, such as digital signal processing, telecommunication devices, reducing network bandwidth usage, and spectral methods for the numerical solution of partial differential equations. The use of cosine rather than sine functions is critical for compression, since it turns out (as described below) that fewer cosine functions are needed to approximate a typical signal, whereas for differential equations the cosines express a particular choice of boundary conditions. In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. The DCTs are generally related to Fourier Series coefficients of a periodically and symmetrically extended sequence whereas DFTs are related to Fourier Series coefficients of only periodically extended sequences. DCTs are equivalent to DFTs of roughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), whereas in some variants the input and/or output data are shifted by half a sample. There are eight standard DCT variants, of which four are common. The most common variant of discrete cosine transform is the type-II DCT, which is often called simply "the DCT". This was the original DCT as first proposed by Ahmed. Its inverse, the type-III DCT, is correspondingly often called simply "the inverse DCT" or "the IDCT". Two related transforms are the discrete sine transform (DST), which is equivalent to a DFT of real and odd functions, and the modified discrete cosine transform (MDCT), which is based on a DCT of overlapping data. Multidimensional DCTs (MD DCTs) are developed to extend the concept of DCT to MD signals. There are several algorithms to compute MD DCT. A variety of fast algorithms have been developed to reduce the computational complexity of implementing DCT. One of these is the integer DCT (IntDCT), an integer approximation of the standard DCT, : ix, xiii, 1, 141–304  used in several ISO/IEC and ITU-T international standards. Notable settings windowper = period for calculation, restricted to powers of 2: "16", "32", "64", "128", "256", "512", "1024", "2048", this reason for this is FFT is an algorithm that computes DFT (Discrete Fourier Transform) in a fast way, generally in 𝑂(𝑁⋅log2(𝑁)) instead of 𝑂(𝑁2). To achieve this the input matrix has to be a power of 2 but many FFT algorithm can handle any size of input since the matrix can be zero-padded. For our purposes here, we stick to powers of 2 to keep this fast and neat. read more about this here: Cooley–Tukey FFT algorithm smthper = smoothing count, this smoothing happens after the first FCT regular pass. this zeros out frequencies from the previously calculated values above SS count. the lower this number, the smoother the output, it works opposite from other smoothing periods Included Alerts Signals Loxx's Expanded Source Types Additional reading A Fast Computational Algorithm for the Discrete Cosine Transform by Chen et al. Practical Fast 1-D DCT Algorithms With 11 Multiplications by Loeffler et al. Cooley–Tukey FFT algorithm
Chỉ báo Pine Script®
của loxx
10
Weighted Burg AR Spectral Estimate Extrapolation of Price [Loxx]Weighted Burg AR Spectral Estimate Extrapolation of Price is an indicator that uses an autoregressive spectral estimation called the Weighted Burg Algorithm. This method is commonly used in speech modeling and speech prediction engines. This method also includes Levinson–Durbin algorithm. As was already discussed previously in the following indicator: Levinson-Durbin Autocorrelation Extrapolation of Price What is Levinson recursion or Levinson–Durbin recursion? In many applications, the duration of an uninterrupted measurement of a time series is limited. However, it is often possible to obtain several separate segments of data. The estimation of an autoregressive model from this type of data is discussed. A straightforward approach is to take the average of models estimated from each segment separately. In this way, the variance of the estimated parameters is reduced. However, averaging does not reduce the bias in the estimate. With the Burg algorithm for segments, both the variance and the bias in the estimated parameters are reduced by fitting a single model to all segments simultaneously. As a result, the model estimated with the Burg algorithm for segments is more accurate than models obtained with averaging. The new weighted Burg algorithm for segments allows combining segments of different amplitudes. The Burg algorithm estimates the AR parameters by determining reflection coefficients that minimize the sum of for-ward and backward residuals. The extension of the algorithm to segments is that the reflection coefficients are estimated by minimizing the sum of forward and backward residuals of all segments taken together. This means a single model is fitted to all segments in one time. This concept is also used for prediction error methods in system identification, where the input to the system is known, like in ARX modeling Data inputs Source Settings: -Loxx's Expanded Source Types. You typically use "open" since open has already closed on the current active bar LastBar - bar where to start the prediction PastBars - how many bars back to model LPOrder - order of linear prediction model; 0 to 1 FutBars - how many bars you want to forward predict BurgWin - weighing function index, rectangular, hamming, or parabolic Things to know Normally, a simple moving average is calculated on source data. I've expanded this to 38 different averaging methods using Loxx's Moving Avreages. This indicator repaints Included Bar color muting Further reading Performance of the weighted burg methods of ar spectral estimation for pitch-synchronous analysis of voiced speech The Burg algorithm for segments Techniques for the Enhancement of Linear Predictive Speech Coding in Adverse Conditions Related Indicators
Chỉ báo Pine Script®
của loxx
3
Synthetic Price Action GeneratorNOTICE: First thing you need to know, it "DOES NOT" reflect the price of the ticker you will load it on. THIS IS NOT AN INDICATOR FOR TRADING! It's a developer tool solely generating random values that look exactly like the fractals we observe every single day. This script's generated candles are as fake as the never ending garbage news cycles we are often force fed and expected to believe by using carefully scripted narratives peddled as hypnotic truth to psychologically and emotionally influence you to the point of control by coercion and subjugation. I wanted to make the script's synthetic nature very clear using that analogy, it's dynamically artificial. Do not accidentally become disillusioned by this scripts values, make trading decisions from it, and lastly don't become victim to predatory media magic ministry parrots with pretty, handsome smiles, compelling you to board their ferris wheel of fear. Now, on to the good stuff... BACKSTORY: Occasionally I find myself in situations where I have to build analyzers in Pine to actually build novel quantitative analytic indicators and tools worthy of future use. These analyzers certainly don't exist on this platform, but usually are required to engineer and tweak algorithms of the highest quality with the finest computational caliber. I have numerous other synthesizers to publish besides this one. For many reasons, I needed a synthetic environment to utilize the analyzers I built in Pine, to even pursue building some exotic indicators and algorithms. Pine doesn't allow sourcing of tuples. Not to mention, I required numerous Pine advancements to make long held dreams into tangible realities. Many Pine upgrades have arrived and MANY, MANY more are in need of implementation for all. Now that I have this, intending to use it in the future often when in need, you can now use it too. I do anticipate some skilled Pine poets will employ this intended handy utility to design and/or improved indicators for trading. ORIGIN: This was inspired by the brilliance from the world renowned ALGOmist John F. Ehlers, but it's taken on a completely alien form from its original DNA. Browsing on the internet for something else, I came across an article with a small code snippet, and I remembered an old wish of mine. I have long known that by flipping back and forth on specific tickers and timeframes in my Watchlist is not the most efficient way to evaluate indicators in multiple theatres of price action. I realized, I always wanted to possess and use this sort of tool, so... I put it into Pine form, but now have decided to inject it with Pine Script steroids. The outcome is highly mutable candle formations in a reusable mutagenic package, observable above and masquerading as genuine looking price candles. OVERVIEW: I guess you could call it a price action synthesizer, but I entitled it "Synthetic Price Action Generator" for those who may be searching for such a thing. You may find this more useful on the All or 5Y charts initially to witness indication from beginning (barstate.isfirst === barindex==0) to end (last_bar_index), but you may also use keyboard shortcuts + + to view the earliest plottable bars on any timeframe. I often use that keyboard shortcut to qualify an indicator through the entirety of it's runtime. A lot can go wrong unexpectedly with indicator initialization, and you will never know it if you don't inspect it. Many recursively endowed Infinite Impulse Response (IIR) Filters can initialize with unintended results that minutely ring in slightly erroneous fashion for the entire runtime, beginning to end, causing deviations from "what should of been..." values with false signals. Looking closely at spg(), you will recognize that 3 EMAs are employed to manage and maintain randomness of CLOSE, HIGH, and LOW. In fact, any indicator's barindex==0 initialization can be inspected with the keyboard shortcuts above. If you see anything obviously strange in an authors indicator, please contact the developer if possible and respectfully notify them. PURPOSE: The primary intended application of this script, is to offer developers from advanced to even novice skill levels assistance with building next generation indicators. Mostly, it's purpose is for testing and troubleshooting indicators AND evaluating how they perform in a "manageable" randomized environment. Some times indicators flake out on rare but problematic price fluctuations, and this may help you with finding your issues/errata sooner than later. While the candles upon initial loading look pristine, by tweaking it to the minval/maxval parameters limits OR beyond with a few code modifications, you can generate unusual volatility, for instance... huge wicks. Limits of minval= and maxval= of are by default set to a comfort zone of operation. Massive wicks or candle bodies will undoubtedly affect your indication and often render them useless on tickers that exhibit that behavior, like WGMCF intraday currently. Copy/paste boundaries are provided for relevant insertion into another script. Paste placement should happen at the very top of a script. Note that by overwriting the close, open, high, etc... values, your compiler will give you generous warnings of "variable shadowing" in abundance, but this is an expected part of applying it to your novel script, no worries. plotcandle() can be copied over too and enabled/disabled in Settings->Style. Always remember to fully remove this scripts' code and those assignments properly before actual trading use of your script occurs, AND specifically when publishing. The entirety of this provided code should never, never exist in a published indicator. OTHER INTENTIONS: Even though these are 100% synthetic generated price points, you will notice ALL of the fractal pseudo-patterns that commonly exist in the markets, are naturally occurring with this generator too. You can also swiftly immerse yourself in pattern recognition exercises with increased efficiency in real time by clicking any SPAG Setting in focus and then using the up/down arrow keys. I hope I explained potential uses adequately... On a personal note, the existence of fractal symmetry often makes me wonder, do we truly live in a totality chaotic universe or is it ordered mathematically for some outcomes to a certain extent. I think both. My observations, it's a pre-deterministic reality completely influenced by infinitesimal amounts of sentient free will with unimaginable existing and emerging quantities. Some how an unknown mysterious mechanism governing the totality of universal physics and mathematics counts this 100.0% flawlessly and perpetually. Anyways, you can't change the past that long existed before your birth or even yesterday, but you can choose to dream, create, and forge the future into your desires and hopes. As always, shite always happens when your not looking for it. What you choose to do after stepping in it unintentionally... is totally up to you. :) Maybe this tool and tips provided will aid you in not stepping in an algo cachucha up to your ankles somehow. SCRIPTING LESSONS PORTRAYED IN THIS SCRIPT: Pine etiquette and code cleanliness Overwrite capabilities of built-in Pine variables for testing indicators Various techniques to organize Settings panel while providing ease of adjustment utility Use of tooltip= to provide users adequate valuable information. Most people want to trade with indicators, not blindly make adjustments to them without any knowledge of their intended operation/effects When available time provides itself, I will consider your inquiries, thoughts, and concepts presented below in the comments section, should you have any questions or comments regarding this indicator. When my indicators achieve more prevalent use by TV members , I may implement more ideas when they present themselves as worthy additions. Have a profitable future everyone!
Chỉ báo Pine Script®
của ImmortalFreedom
18
LinearRegressionLibraryLibrary "LinearRegressionLibrary" contains functions for fitting a regression line to the time series by means of different models, as well as functions for estimating the accuracy of the fit. Linear regression algorithms: RepeatedMedian(y, n, lastBar) applies repeated median regression (robust linear regression algorithm) to the input time series within the selected interval. Parameters: y :: float series, source time series (e.g. close) n :: integer, the length of the selected time interval lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval) Output: mSlope :: float, slope of the regression line mInter :: float, intercept of the regression line TheilSen(y, n, lastBar) applies the Theil-Sen estimator (robust linear regression algorithm) to the input time series within the selected interval. Parameters: y :: float series, source time series n :: integer, the length of the selected time interval lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval) Output: tsSlope :: float, slope of the regression line tsInter :: float, intercept of the regression line OrdinaryLeastSquares(y, n, lastBar) applies the ordinary least squares regression (non-robust) to the input time series within the selected interval. Parameters: y :: float series, source time series n :: integer, the length of the selected time interval lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval) Output: olsSlope :: float, slope of the regression line olsInter :: float, intercept of the regression line Model performance metrics: metricRMSE(y, n, lastBar, slope, intercept) returns the Root-Mean-Square Error (RMSE) of the regression. The better the model, the lower the RMSE. Parameters: y :: float series, source time series (e.g. close) n :: integer, the length of the selected time interval lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval) slope :: float, slope of the evaluated linear regression line intercept :: float, intercept of the evaluated linear regression line Output: rmse :: float, RMSE value metricMAE(y, n, lastBar, slope, intercept) returns the Mean Absolute Error (MAE) of the regression. MAE is is similar to RMSE but is less sensitive to outliers. The better the model, the lower the MAE. Parameters: y :: float series, source time series n :: integer, the length of the selected time interval lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval) slope :: float, slope of the evaluated linear regression line intercept :: float, intercept of the evaluated linear regression line Output: mae :: float, MAE value metricR2(y, n, lastBar, slope, intercept) returns the coefficient of determination (R squared) of the regression. The better the linear regression fits the data (compared to the sample mean), the closer the value of the R squared is to 1. Parameters: y :: float series, source time series n :: integer, the length of the selected time interval lastBar :: integer, index of the last bar of the selected time interval (defines the position of the interval) slope :: float, slope of the evaluated linear regression line intercept :: float, intercept of the evaluated linear regression line Output: Rsq :: float, R-sqared score Usage example: //@version=5 indicator('ExampleLinReg', overlay=true) // import the library import tbiktag/LinearRegressionLibrary/1 as linreg // define the studied interval: last 100 bars int Npoints = 100 int lastBar = bar_index int firstBar = bar_index - Npoints // apply repeated median regression to the closing price time series within the specified interval {square bracket}slope, intercept{square bracket} = linreg.RepeatedMedian(close, Npoints, lastBar) // calculate the root-mean-square error of the obtained linear fit rmse = linreg.metricRMSE(close, Npoints, lastBar, slope, intercept) // plot the line and print the RMSE value float y1 = intercept float y2 = intercept + slope * (Npoints - 1) if barstate.islast {indent} line.new(firstBar,y1, lastBar,y2) {indent} label.new(lastBar,y2,text='RMSE = '+str.format("{0,number,#.#}", rmse))
Thư viện Pine Script®
của tbtkg
6
Cycles StrategyThis is back-testable strategy is a modified version of the Stochastic strategy. It is meant to accompany the modified Stochastic indicator: "Cycles". Modifications to the Stochastic strategy include; 1. Programmable settings for the Stochastic Periods (%K, %D and Smooth %K). 2. Programmable settings for the MACD Periods (Fast, Slow, Smoothing) 3. Programmable thresholds for %K, to qualify a potential entry strategy. 4. Programmable thresholds for %D, to qualify a potential exit strategy. 5. Buttons to choose which components to use in the trading algorithm. 6. Choose the month and year to back test. The trading algorithm: 1. When %K exceeds the upper/lower threshold and then hooks down/up, in the direction of the Moving Average (MA). This is the minimum entry qualification. 2. When %D exceeds the lower/upper threshold and angled in the direction of the trade, is the exit qualification. 3. Additional entry filters include the direction of MACD, Signal and %D. Also, the "cliff", being a long entry is a higher high or a short entry is a lower low. 4. Strategy can only go "Long" or "Short" depending on the selected setting. 5. By matching the settings in the "Cycles" indicator, you can (almost) see what the strategy is doing. 6. Be sure to select the "Recalculate" buttons, to recalculate on every new Tick, for best results. Please click the Like button and leave a comment if you appreciate this script. Improvements will be implemented as time goes on. I am not a licensed trade advisor. This strategy is for entertainment only. Use at your own risk!
Chiến lược Pine Script®
của FXEngineering
Advanced Multi-Level S/R ZonesAdvanced Multi-Level S/R Zones: The Comprehensive Guide 1. Introduction: The Evolution of Support & Resistance: Support and Resistance (S/R) is the backbone of technical analysis. However, traditional methods of drawing these levels are often plagued by subjectivity. Two traders looking at the same chart will often draw two different lines. Furthermore, standard indicators often treat every price point equally, ignoring the critical context of Volume and Time. The Advanced Multi-Level S/R Zones script represents a paradigm shift. It moves away from subjective line drawing and toward Quantitative Zoning. By utilizing statistical measures of variability (Standard Deviation, MAD, IQR) combined with Volume-Weighting and Time-Decay algorithms, this tool identifies where price is mathematically most likely to react. It treats S/R not as thin lines, but as dynamic zones of probability. 2. Core Logic and Mathematical Foundation: To understand how to use this tool optimally, one must understand the "engine" under the hood. The script operates on four distinct pillars of logic: A. Session-Based Data Collection: The script does not look at every single tick. Instead, it aggregates data into "Sessions" (daily bars by default logic). It extracts the High, Low, and Total Volume for every session within the user-defined lookback period. This filters out intraday noise and focuses on the macro structure of the market. B. Adaptive Statistical Variability: Most Bollinger Band-style indicators use Standard Deviation (StdDev) to measure width. However, StdDev is heavily influenced by outliers (extreme wicks). This script offers a sophisticated Adaptive Method-Skewness Detection: The script calculates the skewness of the price distribution. Adaptive Selection: If the data is highly skewed (lots of outliers, typical in Crypto), it switches to MAD (Median Absolute Deviation). MAD is robust and ignores outliers. If the data is moderately skewed, it uses IQR (Interquartile Range). If the data is normal (Gaussian), it uses StdDev. Benefit: This ensures the zone widths are accurate regardless of whether you are trading a stable Forex pair or a volatile Altcoin. C. The Weighting Engine (Volume + Time) Not all price history is equal. This script assigns a "Weight Score" to every session based on two factors: Volume Weighting: Sessions with massive volume (institutional activity) are given higher importance. A high formed on low volume is less significant than a high formed on peak volume. Time Decay: Recent price action is more relevant than price action from 50 bars ago. The script applies a decay factor (default 0.85). This means a session from yesterday has 100% impact, while a session from 10 days ago has significantly less influence on the zone calculation. D. Clustering Algorithm Once the data is weighted, the script runs a clustering algorithm. It looks for price levels where multiple session Highs (for Resistance) or Lows (for Support) congregate. It requires a minimum number of points to form a zone (User Input: minPoints). It merges nearby levels based on the Cluster Separation Factor. This results in "Primary," "Secondary," and "Tertiary" zones based on the strength and quantity of data points in that cluster. 3. Detailed Features and Inputs Breakdown: Group 1: Main Settings Lookback Sessions (Default: 10): Defines how far back the script looks for pivots. A higher number (e.g., 50) creates long-term structural zones. A lower number (e.g., 5) creates short-term scalping zones. Variability Method (Adaptive): As described above, leave this on "Adaptive" for the best results across different assets. Zone Width Multiplier (Default: 0.75): Controls the vertical thickness of the zones. Increase this to 1.0 or 1.5 for highly volatile assets to ensure you catch the wicks. Minimum Points per Zone: The strictness filter. If set to 3, a price level must be hit 3 times within the lookback to generate a zone. Higher numbers = fewer, but stronger zones. Group 2: Weighting Volume-Weighted Zones: Crucial for identifying "Smart Money" levels. Keep this TRUE. Time Decay: Ensures the zones update dynamically. If price moves away from a level for a long time, the zone will fade in significance. ATR-Normalized Zone Width: This is a dynamic volatility filter. If TRUE, the zone width expands and contracts based on the Average True Range. This is vital for maintaining accuracy during market breakouts or crashes. Group 3: Zone Strength & Scoring The script calculates a "Score" (0-100%) for every zone based on: -Point Count: More hits = higher score. -Touches: How many times price wicked into the zone recently. -Intact Status: Has the zone been broken? -Weight: Volume/Time weight of the constituent points. -Track Zone Touches: Looks back n bars to see how often price respected this level. -Touch Threshold: The sensitivity for counting a "touch." Group 4: Visuals & Display Extend Bars: How far to the right the boxes are drawn. Show Labels: Displays the Score, Tier (Primary/Secondary), and Status (Retesting). Detect Pivot Zones (Overlap): This is a killer feature. It detects where a Support Zone overlaps with a Resistance Zone. Significance: These are "Flip Zones" (Old Resistance becomes New Support). They are colored differently (Orange by default) and represent high-probability entry areas. Group 5: Signals & Alerts Entry Signals: Plots Buy/Sell labels when price rejects a zone. Detect Break & Retest: specifically looks for the "Break -> Pullback -> Bounce" pattern, labeled as "RETEST BUY/SELL". Proximity Alert: Triggers when price gets within x% of a zone. 4. Understanding the Visuals (Interpreting the Chart) When you load the script, you will see several visual elements. Here is how to read them: The Boxes (Zones) Red Shades: Resistance Zones. Dark Red (Solid Border): Primary Resistance. The strongest wall. Lighter Red (Dashed Border): Secondary/Tertiary. Weaker, but still relevant. Green Shades: Support Zones. Dark Green (Solid Border): Primary Support. The strongest floor. Orange Boxes: Pivot Zones. These are areas where price has historically reacted as both support and resistance. These are the "Line in the Sand" for trend direction. The Labels & Emojis The script assigns emojis to zone strength: 🔥 (Fire): Score > 80%. A massive level. Expect a strong reaction. ⭐ (Star): Score > 60%. A solid structural level. ✓ (Check): Score > 40%. A standard level. "⟳ RETESTING": Appears when a zone was broken, and price is currently pulling back to test it from the other side. The Dashboard (Top Right) A statistics table provides a "Head-Up Display" for the asset: High/Low σ (Sigma): The variability of the highs and lows. If High σ is much larger than Low σ, it implies the tops are erratic (wicks) while bottoms are clean (flat). Method: Shows which statistical method the Adaptive engine selected (e.g., "MAD (auto)"). ATR: Current volatility value used for normalization. 5. Strategies for Optimum Output To get the most out of this script, you should not just blindly follow the lines. Use these specific strategies: Strategy A: The "Zone Fade" (Range Trading) This works best in sideways markets. Identify a Primary Support (Green) and Primary Resistance (Red). Wait for price to enter the zone. Look for the "SUPPORT BOUNCE" or "RESISTANCE REJECTION" signal label. Entry: Enter against the zone (Buy at support, Sell at resistance). Stop Loss: Place just outside the zone width. Because the zones are calculated using volatility stats, a break of the zone usually means the trade is invalid. Strategy B: The "Pivot Flip" (Trend Following) This is the highest probability setup in trending markets. Look for an Orange Pivot Zone. Wait for price to break through a Resistance Zone cleanly. Wait for the price to return to that zone (which may now turn Orange or act as Support). Look for the "RETEST BUY" label. Logic: Old resistance becoming new support is a classic sign of trend continuation. The script automates the detection of this exact geometric phenomenon. Strategy C: The Volatility Squeeze Look at the Dashboard. Compare High σ and Low σ. If the values are dropping rapidly or becoming very small, the zones will contract (become narrow). Narrow zones indicate a "Squeeze" or compression in price. Prepare for a violent breakout. Do not fade (trade against) narrow zones; look to trade the breakout. 6. Optimization & Customization Guide Different markets require different settings. Here is how to tune the script: For Crypto & Volatile Stocks (Tesla, Nvidia) Method: Set to Adaptive (Mandatory, as these assets have "Fat Tails"). Multiplier: Increase to 1.0 - 1.25. Crypto wicks are deep; you need wider zones to avoid getting stopped out prematurely. Lookback: 20-30 sessions. Crypto has a long memory; short lookbacks generate too much noise. For Forex (EURUSD, GBPJPY) Method: You can force StdDev or IQR. Forex is more mean-reverting and Gaussian. Multiplier: Decrease to 0.5 - 0.75. Forex levels are often very precise to the pip. Volume Weighting: You may turn this OFF for Forex if your broker's volume data is unreliable (since Forex has no centralized volume), though tick volume often works fine. For Scalping (1m - 15m Timeframes) Lookback: Decrease to 5-10. You only care about the immediate session history. Decay Factor: Decrease to 0.5. You want the script to forget about yesterday's price action very quickly. Touch Lookback: Decrease to 20 bars. For Swing Trading (4H - Daily Timeframes) Lookback: Increase to 50. Decay Factor: Increase to 0.95. Structural levels from weeks ago are still highly relevant. Min Points: Increase to 3 or 4. Only show levels that have been tested multiple times. 7. Advantages Over Standard Tools: Feature Standard S/R Indicator, Advanced Multi-Level S/R Calculation, Uses simple Pivots or Fractals, Uses Statistical Distributions (MAD/IQR). Zone Width Arbitrary or Fixed Adaptive based on Volatility & ATR. Context Ignores Volume Volume Weighted (Smart Money tracking). Time Relevance Old levels = New levels Time Decay (Recency bias applied). Overlaps Usually ignores overlaps Detects Pivot Zones (Res/Sup Flip). Scoring None 0-100% Strength Score per zone. 8. Conclusion: The Advanced Multi-Level S/R Zones script is not just a drawing tool; it is a statistical analysis engine. By accounting for the skewness of data, the volume behind the moves, and the decay of time, it provides a strictly objective roadmap of the market structure. For the optimum output, combine the Pivot Zone identification with the Retest Signals. This aligns you with the underlying flow of order blocks and prevents trading against the statistical probabilities of the market.
Chỉ báo Pine Script®
của jaydesaigu
Wavelet Candle Constructor (Inc. Morlet) 2Here is the detailed description of the **Wavelet Candle** construction principles based on the code provided. This indicator is not a simple smoothing mechanism (like a Moving Average). It utilizes the **Discrete Wavelet Transform (DWT)**, specifically the Stationary variant (SWT / à Trous Algorithm), to separate "noise" (high frequencies) from the "trend" (low frequencies). Here is how it works step-by-step: ###1. The Wavelet Kernel (Coefficients)The heart of the algorithm lies in the coefficients (the `h` array in the `get_coeffs` function). Each wavelet type represents a different set of mathematical weights that define how price data is analyzed: * **Haar:** The simplest wavelet. It acts like a simple average of neighboring candles. It reacts quickly but produces a "boxy" or "jagged" output. * **Daubechies 4:** An asymmetric wavelet. It is better at detecting sudden trend changes and the fractal structure of the market, though it introduces a slight phase shift. * **Symlet / Coiflet:** More symmetric than Daubechies. They attempt to minimize lag (phase shift) while maintaining smoothness. * **Morlet (Gaussian):** Implemented in this code as a Gaussian approximation (bell curve). It provides the smoothest, most "organic" effect, ideal for filtering noise without jagged edges. ###2. The Convolution EngineInstead of a simple average, the code performs a mathematical operation called **convolution**: For every candle on the chart, the algorithm takes past prices, multiplies them by the Wavelet Kernel weights, and sums them up. This acts as a **digital low-pass filter**—it allows the main price movements to pass through while cutting out the noise. ###3. The "à Trous" Algorithm (Stationary Wavelet Transform)This is the key difference between this indicator and standard data compression. In a classic wavelet transform, every second data point is usually discarded (downsampling). Here, the **Stationary** approach is used: * **Level 1:** Convolution every **1** candle. * **Level 2:** Convolution every **2** candles (skipping one in between). * **Level 3:** Convolution every **4** candles. * **Level 4:** Convolution every **8** candles. Because of this, **we do not lose time resolution**. The Wavelet Candle is drawn exactly where the original candle is, but it represents the trend structure from a broader perspective. The higher the `Decomposition Level`, the deeper the denoising (looking at a wider context). ###4. Independent OHLC ProcessingThe algorithm processes each component of the candle separately: 1. Filters the **Open** series. 2. Filters the **High** series. 3. Filters the **Low** series. 4. Filters the **Close** series. This results in four smoothed curves: `w_open`, `w_high`, `w_low`, `w_close`. ###5. Geometric Reconstruction (Logic Repair)Since each price series is filtered independently, the mathematics can sometimes lead to physically impossible situations (e.g., the smoothed `Low` being higher than the smoothed `High`). The code includes a repair section: ```pinescript real_high = math.max(w_high, w_low) real_high := math.max(real_high, math.max(w_open, w_close)) // Same logic for Low (math.min) ``` This guarantees that the final Wavelet Candle always has a valid construction: wicks encapsulate the body, and the `High` is strictly the highest point. --- ###Summary of ApplicationThis construction makes the Wavelet Candle an **excellent trend-following tool**. * If the candle is **green**, it means that after filtering the noise (according to the selected wavelet), the market energy is bullish. * If it is **red**, the energy is bearish. * The wicks show volatility that exists within the bounds of the selected decomposition level. Here is a descriptive comparison of **Wavelet Candles** against other popular chart types. As requested, this is a narrative explanation focusing on the differences in mechanics, interpretation philosophy, and the specific pros and cons of each approach. --- ###1. Wavelet Candles vs. Standard (Japanese) CandlesThis is a clash between "the raw truth" and "mathematical interpretation." Standard Japanese candles display raw market data—exactly what happened on the exchange. Wavelet Candles are a synthetic image created by a signal processor. **Differences and Philosophy:** A standard candle is full of emotion and noise. Every single price tick impacts its shape. The Wavelet Candle treats this noise as interference that must be removed to reveal the true energy of the trend. Wavelets decompose the price, reject high frequencies (noise), and reconstruct the candle using only low frequencies (the trend). * **Wavelet Advantages:** The main advantage is clarity. Where a standard chart shows a series of confusing candles (e.g., a long green one, followed by a short red one, then a doji), the Wavelet Candle often draws a smooth, uniform wave in a single color. This makes it psychologically easier to hold a position and ignore temporary pullbacks. * **Wavelet Disadvantages:** The biggest drawback is the loss of price precision. The Open, Close, High, and Low values on a Wavelet candle are calculated, not real. You **cannot** place Stop Loss orders or enter trades based on these levels, as the actual market price might be in a completely different place than the smoothed candle suggests. They also introduce lag, which depends on the chosen wavelet—whereas a standard candle reacts instantly. ###2. Wavelet Candles vs. Heikin AshiThese are close cousins, but they share very different "DNA." Both methods aim to smooth the trend, but they achieve it differently. **Differences and Philosophy:** Heikin Ashi (HA) is based on a simple recursive arithmetic average. The current HA candle depends on the previous one, making it react linearly. The Wavelet Candle uses **convolution**. This means the shape of the current candle depends on a "window" (group) of past candles multiplied by weights (Gaussian curve, Daubechies, etc.). This results in a more "organic" and elastic reaction. * **Wavelet Advantages:** Wavelets are highly customizable. With Heikin Ashi, you are stuck with one algorithm. With Wavelet Candles, you can change the kernel to "Haar" for a fast (boxy) reaction or "Morlet" for an ultra-smooth, wave-like effect. Wavelets handle the separation of market cycles better than simple HA averaging, which can generate many false color flips during consolidation. * **Wavelet Disadvantages:** They are computationally much more complex and harder to understand intuitively ("Why is this candle red if the price is going up?"). In strong, vertical breakouts (pumps), Heikin Ashi often "chases" the price faster, whereas deep wavelet decomposition (High Level) may show more inertia and change color more slowly. ###3. Wavelet Candles vs. RenkoThis compares two different dimensions: Time vs. Price. **Differences and Philosophy:** Renko completely ignores time. A new brick is formed only when the price moves by a specific amount. If the market stands still for 5 hours, nothing happens on a Renko chart. The Wavelet Candle is **time-synchronous**. If the market stands still for 5 hours, the Wavelet algorithm will draw a series of flat, small candles (the "wavelet decays"). * **Wavelet Advantages:** They preserve the context of time, which is crucial for traders who consider trading sessions (London/New York) or macroeconomic data releases. On a wavelet chart, you can see when volatility drops (candles become small), whereas Renko hides periods of stagnation, which can be misleading for options traders or intraday strategies. * **Wavelet Disadvantages:** In sideways trends (chop), Wavelet Candles—despite the smoothing—will still draw a "snake" that flips colors (unless you set a very high decomposition level). Renko can remain perfectly clean and static during the same period, not drawing any new bricks, which for many traders is the ultimate filter against overtrading in a flat market. ###Summary**Wavelet Candles** are a tool for the analyst who wants to visualize the **structure of the wave and market cycle**, accepting some lag in exchange for noise reduction, but without giving up the time axis (like in Renko) or relying on simple averaging (like in Heikin Ashi). It serves best as a "roadmap" for the trend rather than a "sniper scope" for precise entries.
Chỉ báo Pine Script®
của wojlucz
Kalman Filter [DCAUT]█ Kalman Filter 📊 ORIGINALITY & INNOVATION The Kalman Filter represents an important adaptation of aerospace signal processing technology to financial market analysis. Originally developed by Rudolf E. Kalman in 1960 for navigation and guidance systems, this implementation brings the algorithm's noise reduction capabilities to price trend analysis. This implementation addresses a common challenge in technical analysis: the trade-off between smoothness and responsiveness. Traditional moving averages must choose between being smooth (with increased lag) or responsive (with increased noise). The Kalman Filter improves upon this limitation through its recursive estimation approach, which continuously balances historical trend information with current price data based on configurable noise parameters. The key advancement lies in the algorithm's adaptive weighting mechanism. Rather than applying fixed weights to historical data like conventional moving averages, the Kalman Filter dynamically adjusts its trust between the predicted trend and observed prices. This allows it to provide smoother signals during stable periods while maintaining responsiveness during genuine trend changes, helping to reduce whipsaws in ranging markets while not missing significant price movements. 📐 MATHEMATICAL FOUNDATION The Kalman Filter operates through a two-phase recursive process: Prediction Phase: The algorithm first predicts the next state based on the previous estimate: State Prediction: Estimates the next value based on current trend Error Covariance Prediction: Calculates uncertainty in the prediction Update Phase: Then updates the prediction based on new price observations: Kalman Gain Calculation: Determines the weight given to new measurements State Update: Combines prediction with observation based on calculated gain Error Covariance Update: Adjusts uncertainty estimate for next iteration Core Parameters: Process Noise (Q): Represents uncertainty in the trend model itself. Higher values indicate the trend can change more rapidly, making the filter more responsive to price changes. Measurement Noise (R): Represents uncertainty in price observations. Higher values indicate less trust in individual price points, resulting in smoother output. Kalman Gain Formula: The Kalman Gain determines how much weight to give new observations versus predictions: K = P(k|k-1) / (P(k|k-1) + R) Where: K is the Kalman Gain (0 to 1) P(k|k-1) is the predicted error covariance R is the measurement noise parameter When K approaches 1, the filter trusts new measurements more (responsive). When K approaches 0, the filter trusts its prediction more (smooth). This dynamic adjustment mechanism allows the filter to adapt to changing market conditions automatically, providing an advantage over fixed-weight moving averages. 📊 COMPREHENSIVE SIGNAL ANALYSIS Visual Trend Indication: The Kalman Filter line provides color-coded trend information: Green Line: Indicates the filter value is rising, suggesting upward price momentum Red Line: Indicates the filter value is falling, suggesting downward price momentum Gray Line: Indicates sideways movement with no clear directional bias Crossover Signals: Price-filter crossovers generate trading signals: Golden Cross: Price crosses above the Kalman Filter line, suggests potential bullish momentum development, may indicate a favorable environment for long positions, filter will naturally turn green as it adapts to price moving higher Death Cross: Price crosses below the Kalman Filter line, suggests potential bearish momentum development, may indicate consideration for position reduction or shorts, filter will naturally turn red as it adapts to price moving lower Trend Confirmation: The filter serves as a dynamic trend baseline: Price Consistently Above Filter: Confirms established uptrend Price Consistently Below Filter: Confirms established downtrend Frequent Crossovers: Suggests ranging or choppy market conditions Signal Reliability Factors: Signal quality varies based on market conditions: Higher reliability in trending markets with sustained directional moves Lower reliability in choppy, range-bound conditions with frequent reversals Parameter adjustment can help adapt to different market volatility levels 🎯 STRATEGIC APPLICATIONS Trend Following Strategy: Use the Kalman Filter as a dynamic trend baseline: Enter long positions when price crosses above the filter Enter short positions when price crosses below the filter Exit when price crosses back through the filter in the opposite direction Monitor filter slope (color) for trend strength confirmation Dynamic Support/Resistance: The filter can act as a moving support or resistance level: In uptrends: Filter often provides dynamic support for pullbacks In downtrends: Filter often provides dynamic resistance for bounces Price rejections from the filter can offer entry opportunities in trend direction Filter breaches may signal potential trend reversals Multi-Timeframe Analysis: Combine Kalman Filters across different timeframes: Higher timeframe filter identifies primary trend direction Lower timeframe filter provides precise entry and exit timing Trade only in direction of higher timeframe trend for better probability Use lower timeframe crossovers for position entry/exit within major trend Volatility-Adjusted Configuration: Adapt parameters to match market conditions: Low Volatility Markets (Forex majors, stable stocks): Use lower process noise for stability, use lower measurement noise for sensitivity Medium Volatility Markets (Most equities): Process noise default (0.05) provides balanced performance, measurement noise default (1.0) for general-purpose filtering High Volatility Markets (Cryptocurrencies, volatile stocks): Use higher process noise for responsiveness, use higher measurement noise for noise reduction Risk Management Integration: Use filter as a trailing stop-loss level in trending markets Tighten stops when price moves significantly away from filter (overextension) Wider stops in early trend formation when filter is just establishing direction Consider position sizing based on distance between price and filter 📋 DETAILED PARAMETER CONFIGURATION Source Selection: Determines which price data feeds the algorithm: OHLC4 (default): Uses average of open, high, low, close for balanced representation Close: Focuses purely on closing prices for end-of-period analysis HL2: Uses midpoint of high and low for range-based analysis HLC3: Typical price, gives more weight to closing price HLCC4: Weighted close price, emphasizes closing values Process Noise (Q) - Adaptation Speed Control: This parameter controls how quickly the filter adapts to changes: Technical Meaning: Represents uncertainty in the underlying trend model Higher values allow the estimated trend to change more rapidly Lower values assume the trend is more stable and slow-changing Practical Impact: Lower Values: Produces very smooth output with minimal noise, slower to respond to genuine trend changes, best for long-term trend identification, reduces false signals in choppy markets Medium Values: Balanced responsiveness and smoothness, suitable for swing trading applications, default (0.05) works well for most markets Higher Values: More responsive to price changes, may produce more false signals in ranging markets, better for short-term trading and day trading, captures trend changes earlier, adjust freely based on market characteristics Measurement Noise (R) - Smoothing Control: This parameter controls how much the filter trusts individual price observations: Technical Meaning: Represents uncertainty in price measurements Higher values indicate less trust in individual price points Lower values make each price observation more influential Practical Impact: Lower Values: More reactive to each price change, less smoothing with more noise in output, may produce choppy signals Medium Values: Balanced smoothing and responsiveness, default (1.0) provides general-purpose filtering Higher Values: Heavy smoothing for very noisy markets, reduces whipsaws significantly but increases lag in trend change detection, best for cryptocurrency and highly volatile assets, can use larger values for extreme smoothing Parameter Interaction: The ratio between Process Noise and Measurement Noise determines overall behavior: High Q / Low R: Very responsive, minimal smoothing Low Q / High R: Very smooth, maximum lag reduction Balanced Q and R: Middle ground for most applications Optimization Guidelines: Start with default values (Q=0.05, R=1.0) If too many false signals: Increase R or decrease Q If missing trend changes: Decrease R or increase Q Test across different market conditions before live use Consider different settings for different timeframes 📈 PERFORMANCE ANALYSIS & COMPETITIVE ADVANTAGES Comparison with Traditional Moving Averages: Versus Simple Moving Average (SMA): The Kalman Filter typically responds faster to genuine trend changes Produces smoother output than SMA of comparable length Better noise reduction in ranging markets More configurable for different market conditions Versus Exponential Moving Average (EMA): Similar responsiveness but with better noise filtering Less prone to whipsaws in choppy conditions More adaptable through dual parameter control (Q and R) Can be tuned to match or exceed EMA responsiveness while maintaining smoothness Versus Hull Moving Average (HMA): Different noise reduction approach (recursive estimation vs. weighted calculation) Kalman Filter offers more intuitive parameter adjustment Both reduce lag effectively, but through different mechanisms Kalman Filter may handle sudden volatility changes more gracefully Response Characteristics: Lag Time: Moderate and configurable through parameter adjustment Noise Reduction: Good to excellent, particularly in volatile conditions Trend Detection: Effective across multiple timeframes False Signal Rate: Typically lower than simple moving averages in ranging markets Computational Efficiency: Efficient recursive calculation suitable for real-time use Optimal Use Cases: Markets with mixed trending and ranging periods Assets with moderate to high volatility requiring noise filtering Multi-timeframe analysis requiring consistent methodology Systematic trading strategies needing reliable trend identification Situations requiring balance between responsiveness and smoothness Known Limitations: Parameters require adjustment for different market volatility levels May still produce false signals during extreme choppy conditions No single parameter set works optimally for all market conditions Requires complementary indicators for comprehensive analysis Historical performance characteristics may not persist in changing market conditions USAGE NOTES This indicator is designed for technical analysis and educational purposes. The Kalman Filter's effectiveness varies with market conditions, tending to perform better in markets with clear trending phases interrupted by consolidation. Like all technical indicators, it has limitations and should not be used as the sole basis for trading decisions, but rather as part of a comprehensive trading approach. Algorithm performance varies with market conditions, and past characteristics do not guarantee future results. Always test thoroughly with different parameter settings across various market conditions before using in live trading. No technical indicator can predict future price movements with certainty, and all trading involves risk of loss.
Chỉ báo Pine Script®
của DCAUT
ICT SIlver Bullet Trading Windows UK times🎯 Purpose of the Indicator It’s designed to highlight key ICT “macro” and “micro” windows of opportunity, i.e., time ranges where liquidity grabs and algorithmic setups are most likely to occur. The ICT Silver Bullet concept is built on the idea that institutions execute in recurring intraday windows, and these often produce high-probability setups. 🕰️ Windows London Macro Window 10:00 – 11:00 UK time This aligns with a major liquidity window after the London equities open settles and London + EU traders reposition. You’re looking for setups like liquidity sweeps, MSS (market structure shift), and FVG entries here. New York Macro Window 15:00 – 16:00 UK time (10:00 – 11:00 NY time) This is right after the NY equities open, a key ICT window for volatility and liquidity grabs. Power Hour Usually 20:00 – 21:00 UK time (3pm–4pm NY time), the last trading hour of NY equities. ICT often refers to this as another manipulation window where setups can form before the daily close. 🔍 What the Indicator Does Draws session boxes or shading: so you can visually see the London/NY/Power Hour windows directly on your chart. Macro vs. Micro time frames: Macro windows → The ones you set (London & NY) are the major daily algo execution windows. Micro windows → Within those boxes, ICT expects smaller intraday setups (like a Silver Bullet entry from a sweep + FVG). Guides your trade selection: it tells you when not to hunt trades everywhere, but instead to wait for price action confirmation inside those boxes. 🧩 How This Fits ICT Silver Bullet Trading The ICT Silver Bullet strategy says: Wait for one of the macro windows (London or NY). Look for liquidity sweep → market structure shift → FVG. Enter with defined risk inside that hour. This indicator essentially does step 1 for you: it makes those high-probability windows visually obvious, so you don’t waste time trading random hours where algos aren’t active.
Chỉ báo Pine Script®
của muddydefenders
Auto-Fit Growth Trendline# **Theoretical Algorithmic Principles of the Auto-Fit Growth Trendline (AFGT)** ## **🎯 What Does This Algorithm Do?** The Auto-Fit Growth Trendline is an advanced technical analysis system that **automates the identification of long-term growth trends** and **projects future price levels** based on historical cyclical patterns. ### **Primary Functionality:** - **Automatically detects** the most significant lows in regular periods (monthly, quarterly, semi-annually, annually) - **Constructs a dynamic trendline** that connects these historical lows - **Projects the trend into the future** with high mathematical precision - **Generates Fibonacci bands** that act as dynamic support and resistance levels - **Automatically adapts** to different timeframes and market conditions ### **Strategic Purpose:** The algorithm is designed to identify **fundamental value zones** where price has historically found support, enabling traders to: - Identify optimal entry points for long positions - Establish realistic price targets based on mathematical projections - Recognize dynamic support and resistance levels - Anticipate long-term price movements --- ## **🧮 Core Mathematical Foundations** ### **Adaptive Temporal Segmentation Theory** The algorithm is based on **dynamic temporal partition theory**, where time is divided into mathematically coherent uniform intervals. It uses modular transformations to create bijective mappings between continuous timestamps and discrete periods, ensuring each temporal point belongs uniquely to a specific period. **What does this achieve?** It allows the algorithm to automatically identify natural market cycles (annual, quarterly, etc.) without manual intervention, adapting to the inherent periodicity of each asset. The temporal mapping function implements a **discrete affine transformation** that normalizes different frequencies (monthly, quarterly, semi-annual, annual) to a space of unique identifiers, enabling consistent cross-temporal comparative analysis. --- ## **📊 Local Extrema Detection Theory** ### **Multi-Point Retrospective Validation Principle** Local minima detection is founded on **relative extrema theory with sliding window**. Instead of using a simple minimum finder, it implements a cross-validation system that examines the persistence of the extremum across multiple historical periods. **What problem does this solve?** It eliminates false minima caused by temporal volatility, identifying only those points that represent true historical support levels with statistical significance. This approach is based on the **statistical confirmation principle**, where a minimum is only considered valid if it maintains its extremum condition during a defined observation period, significantly reducing false positives caused by transitory volatility. --- ## **🔬 Robust Interpolation Theory with Outlier Control** ### **Contextual Adaptive Interpolation Model** The mathematical core uses **piecewise linear interpolation with adaptive outlier correction**. The key innovation lies in implementing a **contextual anomaly detector** that identifies not only absolute extreme values, but relative deviations to the local context. **Why is this important?** Financial markets contain extreme events (crashes, bubbles) that can distort projections. This system identifies and appropriately weights them without completely eliminating them, preserving directional information while attenuating distortions. ### **Implicit Bayesian Smoothing Algorithm** When an outlier is detected (deviation >300% of local average), the system applies a **simplified Kalman filter** that combines the current observation with a local trend estimation, using a weight factor that preserves directional information while attenuating extreme fluctuations. --- ## **📈 Stabilized Extrapolation Theory** ### **Exponential Growth Model with Dampening** Extrapolation is based on a **modified exponential growth model with progressive dampening**. It uses multiple historical points to calculate local growth ratios, implements statistical filtering to eliminate outliers, and applies a dampening factor that increases with extrapolation distance. **What advantage does this offer?** Long-term projections in finance tend to be exponentially unrealistic. This system maintains short-to-medium term accuracy while converging toward realistic long-term projections, avoiding the typical "exponential explosions" of other methods. ### **Asymptotic Convergence Principle** For long-term projections, the algorithm implements **controlled asymptotic convergence**, where growth ratios gradually converge toward pre-established limits, avoiding unrealistic exponential projections while preserving short-to-medium term accuracy. --- ## **🌟 Dynamic Fibonacci Projection Theory** ### **Continuous Proportional Scaling Model** Fibonacci bands are constructed through **uniform proportional scaling** of the base curve, where each level represents a linear transformation of the main curve by a constant factor derived from the Fibonacci sequence. **What is its practical utility?** It provides dynamic resistance and support levels that move with the trend, offering price targets and profit-taking points that automatically adapt to market evolution. ### **Topological Preservation Principle** The system maintains the **topological properties** of the base curve in all Fibonacci projections, ensuring that spatial and temporal relationships are consistently preserved across all resistance/support levels. --- ## **⚡ Adaptive Computational Optimization** ### **Multi-Scale Resolution Theory** It implements **automatic multi-resolution analysis** where data granularity is dynamically adjusted according to the analysis timeframe. It uses the **adaptive Nyquist principle** to optimize the signal-to-noise ratio according to the temporal observation scale. **Why is this necessary?** Different timeframes require different levels of detail. A 1-minute chart needs more granularity than a monthly one. This system automatically optimizes resolution for each case. ### **Adaptive Density Algorithm** Calculation point density is optimized through **adaptive sampling theory**, where calculation frequency is adjusted according to local trend curvature and analysis timeframe, balancing visual precision with computational efficiency. --- ## **🛡️ Robustness and Fault Tolerance** ### **Graceful Degradation Theory** The system implements **multi-level graceful degradation**, where under error conditions or insufficient data, the algorithm progressively falls back to simpler but reliable methods, maintaining basic functionality under any condition. **What does this guarantee?** That the indicator functions consistently even with incomplete data, new symbols with limited history, or extreme market conditions. ### **State Consistency Principle** It uses **mathematical invariants** to guarantee that the algorithm's internal state remains consistent between executions, implementing consistency checks that validate data structure integrity in each iteration. --- ## **🔍 Key Theoretical Innovations** ### **A. Contextual vs. Absolute Outlier Detection** It revolutionizes traditional outlier detection by considering not only the absolute magnitude of deviations, but their relative significance within the local context of the time series. **Practical impact:** It distinguishes between legitimate market movements and technical anomalies, preserving important events like breakouts while filtering noise. ### **B. Extrapolation with Weighted Historical Memory** It implements a memory system that weights different historical periods according to their relevance for current prediction, creating projections more adaptable to market regime changes. **Competitive advantage:** It automatically adapts to fundamental changes in asset dynamics without requiring manual recalibration. ### **C. Automatic Multi-Timeframe Adaptation** It develops an automatic temporal resolution selection system that optimizes signal extraction according to the intrinsic characteristics of the analysis timeframe. **Result:** A single indicator that functions optimally from 1-minute to monthly charts without manual adjustments. ### **D. Intelligent Asymptotic Convergence** It introduces the concept of controlled asymptotic convergence in financial extrapolations, where long-term projections converge toward realistic limits based on historical fundamentals. **Added value:** Mathematically sound long-term projections that avoid the unrealistic extremes typical of other extrapolation methods. --- ## **📊 Complexity and Scalability Theory** ### **Optimized Linear Complexity Model** The algorithm maintains **linear computational complexity** O(n) in the number of historical data points, guaranteeing scalability for extensive time series analysis without performance degradation. ### **Temporal Locality Principle** It implements **temporal locality**, where the most expensive operations are concentrated in the most relevant temporal regions (recent periods and near projections), optimizing computational resource usage. --- ## **🎯 Convergence and Stability** ### **Probabilistic Convergence Theory** The system guarantees **probabilistic convergence** toward the real underlying trend, where projection accuracy increases with the amount of available historical data, following **law of large numbers** principles. **Practical implication:** The more history an asset has, the more accurate the algorithm's projections will be. ### **Guaranteed Numerical Stability** It implements **intrinsic numerical stability** through the use of robust floating-point arithmetic and validations that prevent overflow, underflow, and numerical error propagation. **Result:** Reliable operation even with extreme-priced assets (from satoshis to thousand-dollar stocks). --- ## **💼 Comprehensive Practical Application** **The algorithm functions as a "financial GPS"** that: 1. **Identifies where we've been** (significant historical lows) 2. **Determines where we are** (current position relative to the trend) 3. **Projects where we're going** (future trend with specific price levels) 4. **Provides alternative routes** (Fibonacci bands as alternative targets) This theoretical framework represents an innovative synthesis of time series analysis, approximation theory, and computational optimization, specifically designed for long-term financial trend analysis with robust and mathematically grounded projections.
Chỉ báo Pine Script®
của didaz
RSI-Adaptive T3 [ChartPrime]The RSI-Adaptive T3 is a precision trend-following tool built around the legendary T3 smoothing algorithm developed by Tim Tillson , designed to enhance responsiveness while reducing lag compared to traditional moving averages. Current implementation takes it a step further by dynamically adapting the smoothing length based on real-time RSI conditions — allowing the T3 to “breathe” with market volatility. This dynamic length makes the curve faster in trending moves and smoother during consolidations. To help traders visualize volatility and directional momentum, adaptive volatility bands are plotted around the T3 line, with visual crossover markers and a dynamic info panel on the chart. It’s ideal for identifying trend shifts, spotting momentum surges, and adapting strategy execution to the pace of the market. HOIW IT WORKS At its core, this indicator fuses two ideas: The T3 Moving Average — a 6-stage recursively smoothed exponential average created by Tim Tillson , designed to reduce lag without sacrificing smoothness. It uses a volume factor to control curvature. A Dynamic Length Engine — powered by the RSI. When RSI is low (market oversold), the T3 becomes shorter and more reactive. When RSI is high (overbought), the T3 becomes longer and smoother. This creates a feedback loop between price momentum and trend sensitivity. // Step 1: Adaptive length via RSI rsi = ta.rsi(src, rsiLen) rsi_scale = 1 - rsi / 100 len = math.round(minLen + (maxLen - minLen) * rsi_scale) pine_ema(src, length) => alpha = 2 / (length + 1) sum = 0.0 sum := na(sum ) ? src : alpha * src + (1 - alpha) * nz(sum ) sum // Step 2: T3 with adaptive length e1 = pine_ema(src, len) e2 = pine_ema(e1, len) e3 = pine_ema(e2, len) e4 = pine_ema(e3, len) e5 = pine_ema(e4, len) e6 = pine_ema(e5, len) c1 = -v * v * v c2 = 3 * v * v + 3 * v * v * v c3 = -6 * v * v - 3 * v - 3 * v * v * v c4 = 1 + 3 * v + v * v * v + 3 * v * v t3 = c1 * e6 + c2 * e5 + c3 * e4 + c4 * e3 The result: an evolving trend line that adapts to market tempo in real-time. KEY FEATURES ⯁ RSI-Based Adaptive Smoothing The length of the T3 calculation dynamically adjusts between a Min Length and Max Length , based on the current RSI. When RSI is low → the T3 shortens, tracking reversals faster. When RSI is high → the T3 stretches, filtering out noise during euphoria phases. Displayed length is shown in a floating table, colored on a gradient between min/max values. ⯁ T3 Calculation (Tim Tillson Method) The script uses a 6-stage EMA cascade with a customizable Volume Factor (v) , as designed by Tillson (1998) . Formula: T3 = c1 * e6 + c2 * e5 + c3 * e4 + c4 * e3 This technique gives smoother yet faster curves than EMAs or DEMA/Triple EMA. ⯁ Visual Trend Direction & Transitions The T3 line changes color dynamically: Color Up (default: blue) → bullish curvature Color Down (default: orange) → bearish curvature Plot fill between T3 and delayed T3 creates a gradient ribbon to show momentum expansion/contraction. Directional shift markers (“🞛”) are plotted when T3 crosses its own delayed value — helping traders spot trend flips or pullback entries. ⯁ Adaptive Volatility Bands Optional upper/lower bands are plotted around the T3 line using a user-defined volatility window (default: 100). Bands widen when volatility rises, and contract during compression — similar to Bollinger logic but centered on the adaptive T3. Shaded band zones help frame breakout setups or mean-reversion zones. ⯁ Dynamic Info Table A live stats panel shows: Current adaptive length Maximum smoothing (▲ MaxLen) Minimum smoothing (▼ MinLen) All values update in real time and are color-coded to match trend direction. HOW TO USE Use T3 crossovers to detect trend transitions, especially during periods of volatility compression. Watch for volatility contraction in the bands — breakouts from narrow band periods often precede trend bursts. The adaptive smoothing length can also be used to assess current market tempo — tighter = faster; wider = slower. CONCLUSION RSI-Adaptive T3 modernizes one of the most elegant smoothing algorithms in technical analysis with intelligent RSI responsiveness and built-in volatility bands. It gives traders a cleaner read on trend health, directional shifts, and expansion dynamics — all in a visually efficient package. Perfect for scalpers, swing traders, and algorithmic modelers alike, it delivers advanced logic in a plug-and-play format.
Chỉ báo Pine Script®
của ChartPrime
12
[blackcat] L2 Multi-Level Price Condition TrackerOVERVIEW The L2 Multi-Level Price Condition Tracker represents an innovative approach to analyzing financial markets by simultaneously monitoring multiple price levels, thus providing traders with a holistic view of market dynamics. By combining dynamic calculations based on moving averages and price deviations, this tool aims to deliver precise and actionable insights into potential entry and exit points. It leverages sophisticated statistical measures to identify key thresholds that signify shifts in market sentiment, thereby aiding traders in making well-informed decisions. 🎯 Key benefits encompass: • Comprehensive calculation of midpoints and average prices indicating short-term trend directions. • Interactive visualization elements enhancing interpretability effortlessly. • Real-time generation of buy/sell signals driven by precise condition evaluations. TECHNICAL ANALYSIS COMPONENTS 📉 Midpoint Calculations: Computes central reference points derived from high-low ranges establishing baseline supports/resistances. Utilizes Simple Moving Averages (SMAs) along with standardized deviation formulas smoothing out volatility while preserving long-term trends accurately. Facilitates identification of directional biases reflecting underlying market forces dynamically. 🕵️‍♂️ Advanced Price Level Detection: Derives upper/lower bounds adjusting sensitivities adaptively responding to changing conditions flexibly. Employs proprietary logic distinguishing between bullish/bearish sentiments promptly signaling transitions effectively. Ensures consistent adherence to predefined statistical protocols maintaining accuracy robustly. 🎥 Dynamic Signal Generation: Detects crossovers indicating dominance shifts between buyers/sellers promptly triggering timely alerts. Integrates conditional logic reinforcing signal validity minimizing erroneous activations systematically. Supports adaptive thresholds tuning sensitivities based on evolving market conditions flexibly accommodating varying scenarios. INDICATOR FUNCTIONALITY 🔢 Core Algorithms: Utilizes moving averages alongside standardized deviation formulas generating precise net volume measurements. Implements Arithmetic Mean Line Algorithm (AMLA) smoothing techniques improving interpretability. Ensures consistent alignment with established statistical principles preserving fidelity. 🖱️ User Interface Elements: Dedicated plots displaying real-time midpoint markers facilitating swift decision-making. Context-sensitive color coding distinguishing positive/negative deviations intuitively highlighting key activations clearly. Background shading emphasizing proximity to crucial threshold activations enhancing visibility focusing attention on vital signals promptly. STRATEGY IMPLEMENTATION ✅ Entry Conditions: Confirm bullish/bearish setups validated through multiple confirmatory signals assessing concurrent market sentiment factors. Validate entry decisions considering alignment between calculated midpoints and broader trend directions ensuring coherence. Monitor cumulative breaches signifying potential trend reversals executing partial/total closes contingent upon predetermined loss limits preserving capital efficiently. 🚫 Exit Mechanisms: Trigger exits upon hitting predefined thresholds derived from historical analyses promptly executing closures. Execute partial/total closes contingent upon cumulative loss limits preserving capital efficiently managing exposures prudently. Conduct periodic reviews gauging strategy effectiveness rigorously identifying areas needing refinement implementing corrective actions iteratively enhancing performance metrics steadily. PARAMETER CONFIGURATIONS 🎯 Optimization Guidelines: Lookback Period: Governs responsiveness versus stability balancing sensitivity/stability governing moving averages aligning with preferred granularity. Price Source: Dictates primary data series driving volume calculations selecting relevant inputs accurately tailoring strategies accordingly. 💬 Customization Recommendations: Commence with baseline defaults; iteratively refine parameters isolating individual impacts evaluating adjustments independently prior to combined modifications minimizing disruptions. Prioritize minimizing erroneous trigger occurrences first optimizing signal fidelity sustaining balanced risk-reward profiles irrespective of chosen settings upholding disciplined approaches preserving capital efficiently. ADVANCED RISK MANAGEMENT 🛡️ Proactive Risk Mitigation Techniques: Enforce strict compliance with pre-defined maximum leverage constraints adhering strictly to guidelines managing exposures prudently. Mandatorily apply trailing stop-loss orders conforming to script outputs enforcing discipline rigorously preventing adverse consequences. Allocate positions proportionately relative to available capital reserves conducting periodic reviews gauging effectiveness continuously identifying improvement opportunities steadily. ⚠️ Potential Pitfalls & Solutions: Address frequent violations arising during heightened volatility phases necessitating manual interventions judiciously preparing contingency plans proactively mitigating risks effectively. Manage false alerts warranting immediate attention avoiding adverse consequences systematically implementing corrective actions reliably. Prepare proactive responses amid adverse movements ensuring seamless functionality amidst fluctuating conditions fortifying resilience against anomalies robustly. PERFORMANCE MONITORING METRICS 🔍 Evaluation Criteria: Assess win percentages consistently across diverse trading instruments gauging reliability measuring profitability efficiency accurately evaluating downside risks comprehensively uncovering systematic biases potentially skewing outcomes. Calculate average profit ratios per successful execution benchmarking actual vs expected performances documenting results meticulously tracking progress dynamically addressing identified shortcomings proactively fostering continuous improvements. 📈 Historical Data Analysis Tools: Maintain detailed logs capturing every triggered event recording realized profits/losses comparing simulated projections accurately identifying discrepancies warranting investigation implementing iterative refinements steadily enhancing performance metrics progressively. Identify recurrent systematic errors demanding corrective actions implementing iterative refinements steadily addressing identified shortcomings proactively fostering continuous enhancements dynamically improving robustness resiliently. PROBLEM SOLVING ADVICE 🔧 Frequent Encountered Challenges: Unpredictable behaviors emerging within thinly traded markets requiring filtration processes enhancing signal integrity excluding low-liquidity assets prone to erratic movements effectively. Latency issues manifesting during abrupt price fluctuations causing missed opportunities introducing buffer intervals safeguarding major news/event impacts mitigating distortions seamlessly verifying reliable connections ensuring uninterrupted data flows guaranteeing accurate interpretations dependably. 💡 Effective Resolution Pathways: Limit ongoing optimization attempts preventing model degradation maintaining optimal performance levels consistently recalibrating parameters periodically adapting strategies flexibly responding appropriately amidst varying conditions dynamically improving robustness resiliently. Verify reliable connections ensuring uninterrupted data flows guaranteeing accurate interpretations dependably bolstering overall efficacy systematically addressing identified shortcomings dynamically fostering continuous advancements. THANKS Heartfelt acknowledgment extends to all developers contributing invaluable insights regarding multi-level price condition-based trading methodologies! ✨
Chỉ báo Pine Script®
của blackcat1402
[blackcat] L2 Z-Score of PriceOVERVIEW The L2 Z-Score of Price indicator offers traders an insightful perspective into how current prices diverge from their historical norms through advanced statistical measures. By leveraging Z-scores, it provides a robust framework for identifying potential reversals in financial markets. The Z-score quantifies the number of standard deviations that a data point lies away from the mean, thus serving as a critical metric for recognizing overbought or oversold conditions. 🎯 Key benefits encompass: • Precise calculation of Z-scores reflecting true price deviations. • Interactive plotting features enhancing visual clarity. • Real-time generation of buy/sell signals based on crossover events. STATISTICAL ANALYSIS COMPONENTS 📉 Mean Calculation: Utilizes Simple Moving Averages (SMAs) to establish baseline price references. Provides smooth representations filtering short-term noise preserving long-term trends. Fundamental for deriving subsequent deviation metrics accurately. 📈 Standard Deviation Measurement: Quantifies dispersion around established means revealing underlying variability. Crucial for assessing potential volatility levels dynamically adapting strategies accordingly. Facilitates precise Z-score derivations ensuring statistical rigor. 🕵️‍♂️ Z-SCORE DETECTION: Measures standardized distances indicating relative positions within distributions. Helps pinpoint extreme conditions signaling impending reversals proactively. Enables early identification of trend exhaustion phases prompting timely actions. INDICATOR FUNCTIONALITY 🔢 Core Algorithms: Integrates SMAs along with standardized deviation formulas generating precise Z-scores. Employs Arithmetic Mean Line Algorithm (AMLA) smoothing techniques improving interpretability. Ensures consistent adherence to predefined statistical protocols maintaining accuracy. 🖱️ User Interface Elements: Dedicated plots displaying real-time Z-score markers facilitating swift decision-making. Context-sensitive color coding distinguishing positive/negative deviations intuitively. Background shading highlighting proximity to key threshold activations enhancing visibility. STRATEGY IMPLEMENTATION ✅ Entry Conditions: Confirm bullish/bearish setups validated through multiple confirmatory signals. Validate entry decisions considering concurrent market sentiment factors. Assess alignment between Z-score readings and broader trend directions ensuring coherence. 🚫 Exit Mechanisms: Trigger exits upon hitting predetermined thresholds derived from historical analyses. Monitor continuous breaches signifying potential trend reversals promptly executing closures. Execute partial/total closes contingent upon cumulative loss limits preserving capital efficiently. PARAMETER CONFIGURATIONS 🎯 Optimization Guidelines: Length: Governs responsiveness versus smoothing trade-offs balancing sensitivity/stability. Price Source: Dictates primary data series driving Z-score computations selecting relevant inputs accurately. 💬 Customization Recommendations: Commence with baseline defaults; iteratively refine parameters isolating individual impacts. Evaluate adjustments independently prior to combined modifications minimizing disruptions. Prioritize minimizing erroneous trigger occurrences first optimizing signal fidelity. Sustain balanced risk-reward profiles irrespective of chosen settings upholding disciplined approaches. ADVANCED RISK MANAGEMENT 🛡️ Proactive Risk Mitigation Techniques: Enforce strict compliance with pre-defined maximum leverage constraints adhering strictly to guidelines. Mandatorily apply trailing stop-loss orders conforming to script outputs reinforcing discipline. Allocate positions proportionately relative to available capital reserves managing exposures prudently. Conduct periodic reviews gauging strategy effectiveness rigorously identifying areas needing refinement. ⚠️ Potential Pitfalls & Solutions: Address frequent violations arising during heightened volatility phases necessitating manual interventions judiciously. Manage false alerts warranting immediate attention avoiding adverse consequences systematically. Prepare contingency plans mitigating margin call possibilities preparing proactive responses effectively. Continuously assess automated system reliability amidst fluctuating conditions ensuring seamless functionality. PERFORMANCE AUDITS & REFINEMENTS 🔍 Critical Evaluation Metrics: Assess win percentages consistently across diverse trading instruments gauging reliability. Calculate average profit ratios per successful execution measuring profitability efficiency accurately. Measure peak drawdown durations alongside associated magnitudes evaluating downside risks comprehensively. Analyze signal generation frequencies revealing hidden patterns potentially skewing outcomes uncovering systematic biases. 📈 Historical Data Analysis Tools: Maintain comprehensive records capturing every triggered event meticulously documenting results. Compare realized profits/losses against backtested simulations benchmarking actual vs expected performances accurately. Identify recurrent systematic errors demanding corrective actions implementing iterative refinements steadily. Document evolving performance metrics tracking progress dynamically addressing identified shortcomings proactively. PROBLEM SOLVING ADVICE 🔧 Frequent Encountered Challenges: Unpredictable behaviors emerging within thinly traded markets requiring filtration processes. Latency issues manifesting during abrupt price fluctuations causing missed opportunities. Overfitted models yielding suboptimal results post-extensive tuning demanding recalibrations. Inaccuracies stemming from incomplete/inaccurate data feeds necessitating verification procedures. 💡 Effective Resolution Pathways: Exclude low-liquidity assets prone to erratic movements enhancing signal integrity. Introduce buffer intervals safeguarding major news/event impacts mitigating distortions effectively. Limit ongoing optimization attempts preventing model degradation maintaining optimal performance levels consistently. Verify reliable connections ensuring uninterrupted data flows guaranteeing accurate interpretations reliably. USER ENGAGEMENT SEGMENT 🤝 Community Contributions Welcome Highly encourage active participation sharing experiences & recommendations!
Chỉ báo Pine Script®
của blackcat1402