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Wavelet Energy OscillatorWavelet Energy Oscillator What it does The Wavelet Energy Oscillator decomposes price into three cycle bands at once — fast, mid and slow — and shows two things together: a single composite momentum line (in σ units) and a live energy spectrum telling you which band currently drives the market. Why this is different (and original) Cycle and dominant-period tools lock onto one period and follow it. The problem is that markets hand control between timescales: a fast, choppy regime gives way to a slower swing, and a single-period reading only turns after that has happened. By running a bank of band-pass filters in parallel and measuring the energy in each band, this oscillator shows the whole spectrum simultaneously — so a fast band losing energy to a slow band is visible as an early footprint of a regime change. Presenting the live energy split next to a dominant-band-coloured composite, with a built-in edge test, is what makes it original. How it works Three band-pass filters (recursive, near-orthogonal) are centred on the fast, mid and slow periods you choose. Each band's energy is its smoothed squared output. The three energies are normalized to percentage shares so the dashboard reads as a live spectrum. The composite is the summed band output, z-scored over the normalization window into the σ oscillator and coloured by whichever band currently dominates. How to use it Read the spectrum first. Fast share dominant → short, choppy moves; slow share dominant → a longer swing is in control; a shift between them flags a changing regime. Composite zero-crosses (triangles) time the swing in the dominant band; the σ bands (red top, green bottom) flag stretched readings. The line's colour tells you which timeframe is driving at a glance. Read the EDGE row. The harness checks whether composite crosses preceded a favourable ≥ k×ATR move within the horizon, versus the unconditional Base %. EDGE = Hit − Base. Settings guide 01 · Cycle Bands — source, the three centre periods, bandwidth (narrow = sharper/ringier, wide = smoother), energy smoothing, universal price source. 02 · Normalization — z-score window, output smoothing. 03 · Calibration — horizon, favourable-move threshold (×ATR), base-rate window. 04 · Bands — swing and extreme σ bands. 05 · Display & Theme — visual style, regime tint, dashboard, and per-band + band-zone colors. Non-repaint All filters are recursive and run on closed bars — no recalculation of history, no future leak. Concept credit Band-pass / roofing digital-signal-processing filters for market cycles — John Ehlers, Cycle Analytics for Traders (2013) and Rocket Science for Traders (2001). Disclaimer For research and education only. Not financial advice, not a recommendation, and not a guarantee of future results. Market cycles are non-stationary — band energy describes the recent spectrum, it does not predict it. All statistics are in-sample, close-to-close, and exclude costs. Do your own research and manage your own risk.
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của Market_Logic_India
Hilbert Bandwidth [LB]🔬 Concept The Hilbert Bandwidth Index, derived from John Ehlers' analytic signal approach, measures the instantaneous stability of the dominant market cycle by computing the bandwidth — the absolute deviation between the raw instantaneous period and its smoothed counterpart. A narrow bandwidth indicates a clean, well-defined cycle suitable for trading. 📐 Mathematical Foundation The price median is transformed via a 7‑coefficient FIR Hilbert Transform to extract the analytic signal's real and imaginary components : real = 0.0962·P + 0.5769·P - 0.5769·P - 0.0962·P imag = 0.0962·P + 0.5769·P - 0.5769·P - 0.0962·P The instantaneous phase φ is obtained via the two‑argument arctangent of imag and real . After exponential smoothing, the phase difference Δφ between consecutive bars yields the instantaneous period : T = 2π / |Δφ| Finally, the bandwidth is defined as : B = |T - EMA(T, L) | where L is the period smoothing length. The result is expressed in bars. 🎯 What Problem Does It Solve ? Traditional cycle indicators assume a persistent dominant cycle, producing unreliable signals during chaotic or transitional markets — the Hilbert Bandwidth quantifies cycle cleanliness in real time, allowing traders to filter out low‑quality cyclic signals and act only when the market exhibits a stable, tradeable rhythm. 📊 How To Interpret Bandwidth below threshold (background colored) → the dominant cycle is narrow, well‑defined, and stable ; trend‑following and cycle‑based strategies have higher probability of success. Bandwidth above threshold → the cycle is broad and unstable ; the market is either noisy or in transition ; avoid cycle‑dependent entries. Bandwidth rapidly contracting → the market is shifting from chaos to order ; anticipate a breakout or the emergence of a clean trend. ⚙️ Parameters Phase Smoothing – exponential smoothing length applied to the instantaneous phase (default 50) ; higher values stabilize the phase estimate but introduce lag. Period Smoothing – EMA length applied to the instantaneous period (default 10) ; controls the responsiveness of the bandwidth calculation. Narrow Band Threshold – the bandwidth value in bars below which the cycle is considered "clean" (default 3.0) ; the background is highlighted when bandwidth falls below this level. 📚 Reference Ehlers J.F., "Rocket Science for Traders : Digital Signal Processing Applications", Chapter 7 – The Hilbert Transform, John Wiley & Sons, 2001. Ehlers J.F., "Cycle Analytics for Traders", Chapter 9 – Bandwidth Measurement, John Wiley & Sons, 2014.
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của luis_barlier
Ehlers Decycler Oscillator [NovaLens]Adaptive momentum oscillator built to separate two things most oscillators blur together: cycle rotation and distribution extremes. Auto-detects the dominant cycle, grades the oscillator against its own rolling history, and highlights confluence when both channels align. Most oscillators conflate "the swing is high" with "the swing is reversing." They use the same colour, the same arrow, the same alert for both. The Decycler Oscillator separates them by design: Cycle channel tracks WHERE the swing is in its rotation (Rising / Topping / Falling / Bottoming). Distribution channel tracks WHERE the value sits in its own rolling history (Upper Extreme / Upper / Lower / Lower Extreme). A reading at the upper extreme of the distribution is not a sell signal. It is the market saying "this is rare for me." Whether it actually reverses depends on the cycle channel. When both channels agree (a cycle turn happening right at a distribution extreme), that is the confluence event. Everything else is partial information, and the indicator says so. ════════════════════════════════════════════ ◉ HOW IT WORKS The filter. The core is John Ehlers' Decycler Oscillator (Cycle Analytics for Traders, 2013): a two-stage high-pass filter that strips the slow trend out of price and leaves the swing component. We run two of them in parallel (Fast at the dominant period, Slow at 1.25x) and read crossovers as cycle turns. The adaptive period. The dominant period itself is detected, not assumed. On the Adaptive profile, an Autocorrelation Periodogram (Ehlers, 2016) scans a timeframe-derived range every bar, pulls the strongest cycle by power-weighted centre of gravity, and feeds that period into the filter. Scan range auto-tunes to the chart timeframe: 8-30 bars on intraday, 20-60 on daily and above. Fixed profiles (Reactive / Balanced / Smooth) skip the scan and lock the period for traders who already know the rhythm of their asset. The rank window. The output is percentile-ranked over a rolling window (about 2x cycle period) to produce the four-tier distribution grade. The window LOCKS on confirmed zero-line crosses. A mid-swing period shift cannot silently shrink the window and produce phantom Upper Extreme reads. That single lock helps keep the percentile grade more stable across regime transitions. ════════════════════════════════════════════ ◈ HOW TO READ IT The pane shows two lines (Fast and Slow) wrapped in a ribbon coloured by the current distribution tier: Teal: Upper Extreme Dark teal: Upper Burgundy: Lower Red: Lower Extreme Markers, in order of conviction: Cycle Cross (small triangle): Fast crossed Slow in a tier-aligned direction. "Cycle just flipped." Mid-tier crosses are filtered out as chop noise. Reversal Confluence (large triangle): a cycle cross within 0-2 bars of a same-side exhaustion signal. Both channels agreed. This is the primary event the indicator is built around. Exhaustion (small circle, colour inverted ): oscillator peaked or troughed at the extreme of its rolling distribution. Colour is inverted by design to make exhaustion easier to read. A RED peak means upside pressure may be cooling. A GREEN trough means downside pressure may be fading. Distribution extremes are non-directional information. Continuation (Bull/Bear pill, small rounded label "Bull" / "Bear"): hidden divergence. Oscillator made a lower trough while close made a higher close (Bull), or oscillator made a higher peak while close made a lower close (Bear). This can support a continuation read rather than a reversal read. The info panel (top right by default) synthesises all five channels into one Setup line: Strong Bull/Bear Setup, Continuation Forming, Topping/Bottoming, Trend Running Up/Down, Stretched, Drift, or Quiet, in priority order. ════════════════════════════════════════════ ✦ HOW WE USE IT: CONFLUENCE OVER CROSSES A common pattern on a liquid futures or crypto chart, Adaptive profile: ribbon goes Lower Extreme as price drops into a support zone. Lower Exhaustion fires (green circle, candle border tints orange). Within 2 bars, Fast crosses up through Slow, and a Reversal Confluence triangle prints below the ribbon. The Setup row reads "Strong bull setup." Tier transitions back through Lower into Upper on the next leg up. That is the indicator doing its job: telling you the cycle and the distribution channels both agreed, in the same direction, within the same 2-bar window. Without confluence, the same cycle cross can appear frequently in choppy conditions and often carries less value on its own. Confluence is designed to reduce low-quality cycle flips by gating on the distribution extreme. The Continuation pill addresses a different problem: spotting possible trend resumption. On a pullback within an uptrend, price holds a higher low while the oscillator prints a lower trough. That is hidden bullish divergence, which can support a continuation read rather than a reversal read. The indicator draws a small Bull pill below the ribbon. Built to be read quickly. ════════════════════════════════════════════ ✦ OTHER APPLICATIONS Reversal context : confluence triangles after a cycle turn at the distribution extreme, optionally combined with the Setup row reading Strong Bull/Bear Setup Trend continuation : Bull/Bear pills inside a clean directional move, used as continuation context inside an existing trend plan Distribution awareness : Upper Extreme / Lower Extreme tier reads as a "rare for this market" cue, layered on top of any external trade plan Cycle phase tracking : the info-panel Phase row (Rising / Topping / Falling / Bottoming) as a regime descriptor for higher-timeframe positioning Alert-driven workflow : subscribe to confluence and exhaustion alerts to reduce chart-watching and focus only on higher-priority events ════════════════════════════════════════════ ⚙ GETTING STARTED The Ehlers Decycler Oscillator ships with practical starting profiles: Adaptive (default): Autocorrelation Periodogram detects the dominant cycle every bar. Useful when the asset's typical cycle is unclear. Reactive : HP Period 40, faster turns. Use on shorter timeframes or fast-moving instruments. Balanced : HP Period 80, middle ground. A reasonable starting point on most assets if you want a fixed period. Smooth : HP Period 125, slower turns. Use on higher timeframes or when you want only larger-scale rotations. Custom : full manual control of HP Period and Rank Window. Core settings: Profile : selects the tuning bundle above. Start with Adaptive. HP Period (Custom) : dominant cycle the filter targets, in BARS. 80 means 80 candles. The calendar time depends on the market and timeframe. Longer = smoother, fewer turns; shorter = more reactive. Rank Window (Custom) : rolling lookback for the 4-tier percentile grade. Rule of thumb: about 2x HP Period. Min/Max Period Override (Adaptive) : clamp the cycle scan range. 0 = auto-derive from chart timeframe. Continuation settings: Show Bull/Bear (Continuation) : toggle the hidden-divergence pills. Max Lookback (Continuation) : bars between the two extremes that define a continuation pattern. 0 = auto: 2x average cycle once 3 cycles confirm, else 40. Marker settings: Show Cycle Crosses / Show Confluence Crosses : independent toggles. Turn cycle crosses OFF and confluence ON to see only primary confluence events. Show Exhaustion : distribution-extreme circles on the ribbon. Colour INVERTED by design. Show Price Chart Markers : mirrors confluence and exhaustion onto the price chart. Display: Show Info Panel : 5-row panel (Tier / Phase / Exhaustion / Setup / Cycle). On by default. Light Theme Mode : swap info-panel colours for light chart backgrounds. ════════════════════════════════════════════ △ LIMITATIONS Warm-up : Adaptive needs a brief warm-up period (typically 40-80 bars depending on timeframe) before the cycle scan returns confident readings. Until then, the info panel shows "warming up..." and signals are suppressed. Choppy markets : when the autocorrelation power drops below 0.5, the cycle confidence is "Low" and the indicator says so. Weak signal tends to produce noisy reads. Adaptive period drift : fast HP-period changes can make the oscillator amplitude jump. The alpha-smoothing pass softens this, but in extreme regime shifts the first 5-10 bars after a shift may read noisier. Fixed profiles bypass cycle confidence : Reactive / Balanced / Smooth do not run the cycle scan, so they cannot tell you when the rhythm is unclear. Adaptive can. Continuation needs at least 8 bars between extremes : pivots closer than that are filtered as noise. On very fast intraday timeframes this can suppress otherwise-valid patterns. Continuation in parabolic moves : hidden divergence can chain-fire on blow-off legs because momentum stays pinned at the extreme while price continues to expand, marking same-direction pills back-to-back when momentum is overstretched. They remain continuation reads, not exhaustion warnings. ════════════════════════════════════════════ 🔔 ALERTS Ten alert conditions are built in so you can monitor without checking every bar manually: Upper Exhaustion / Lower Exhaustion : oscillator peaked or troughed at the extreme of its rolling distribution. The RED-at-top, GREEN-at-bottom inversion still applies. Topping / Bottoming : cycle phase transitioned (Rising to Topping, or Falling to Bottoming). Bull Cross / Bear Cross : Fast crossed Slow in a tier-aligned direction without a same-side exhaustion in the prior 2 bars. Bull Cross Confluence / Bear Cross Confluence : Fast crossed Slow within 2 bars of a same-side exhaustion signal. The main confluence event. Bull Continuation / Bear Continuation : hidden-divergence pattern confirmed (oscillator and price disagreement in the trend direction). All ten alerts fire on bar close (gated on barstate.isconfirmed). Each alert message includes ticker, price, timeframe, and timestamp placeholders for webhook routing. ════════════════════════════════════════════ ⌁ NOTES The original Decycler Oscillator construction was developed against a Python reference implementation under PyneCore. Repaint: intrabar-only. Closed-bar alerts are confirmed; current-bar visuals may update until the bar closes. All alert conditions are gated on barstate.isconfirmed. References: John F. Ehlers, Cycle Analytics for Traders (2013), Wiley; Ehlers, Autocorrelation Periodogram (Stocks & Commodities, 2016). Open-source under MPL 2.0. Free to use, fork, study. NovaLens
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của NovaLens
1
Trend Sniper v2.5 [Jamallo](2025) Intro Trend Sniper v2.5 is built around a novel-unique core construction — the Butterworth Stop : a ratcheting trailing stop anchored to a 2-Pole Butterworth Super Smoother and dynamically sized by Parkinson Volatility. While each algorithm used is individually well-documented, this specific combination is rare and not found in standard indicator libraries — most Butterworth implementations are simply plotted as trend lines, not used as the structural anchor of a volatility-adaptive stop mechanism. Break down: 2-Pole Butterworth Super Smoother (Core Trend Line) (smoothed price) The backbone of the indicator is a 2-Pole Butterworth Super Smoother, a concept brought into trading by engineer and author John Ehlers, first published in his 2004 book Cybernetic Analysis for Stocks and Futures In this indicator: The Butterworth filter runs on close with a user-defined period (default 20) and produces bw_trend — a clean, lag-minimized version of price. This smoothed value is not plotted directly. Instead, it acts as the anchor point for the trailing stop. The stop is placed at bw_trend ± stop_dist , meaning the stop hugs the filtered trend rather than raw price, making it far less susceptible to wick noise and erratic bars. Without this pre-filtering step, the trailing stop would oscillate erratically on volatile bars. Parkinson Volatility (Sizes the Stop Distance) "Developed by physicist Michael Parkinson in 1980, it estimates volatility using the natural logarithm of the high-to-low ratio each period, capturing intraday range rather than just close-to-close movement." In this indicator: Parkinson Volatility is calculated over a rolling window (default 50 bars) and multiplied by stop_mult (default 1.2) to produce stop_dist . When markets are volatile, stop_dist expands and the stop gives price more room. When markets are quiet, it contracts and the stop tightens. Butterworth Stop State Machine (The Main Line You Watch) This is the primary plotted line, It's a classic ratcheting trailing stop built on top of outputs from steps 1 and 2. In this indicator: The logic is a simple state machine with two modes — uptrend and downtrend. In an uptrend, the stop only moves up (never down), tracking at bw_trend − stop_dist . In a downtrend, it only moves down, tracking at bw_trend + stop_dist . When price closes on the wrong side of the stop, the state flips and the stop resets on the other side of the trend line. Because both the anchor bw_trend and the buffer stop_dist are noise-filtered and volatility-adjusted, the BW Stop flips far less often than a raw price-based trailing stop would, keeping you in trends longer. Chande Momentum Oscillator + Deadband (Colors the BW Stop Line) "The CMO measures momentum by calculating the difference between the sum of gains and the sum of losses over a specified period, dividing by their total to produce a normalized scale from -100 to +100 that accounts for both up and down days simultaneously." In this indicator: CMO is calculated on bw_stop itself (not raw price), over 14 bars by default. A deadband of ±10 is applied — the line only turns bull-colored when CMO exceeds +10, and bear-colored when it drops below −10. It does not change color in between. KAMA Midpoint (The Dynamic Midline and Fill Zone Anchor) "Introduced by Perry Kaufman in 1995, KAMA dynamically adjusts its smoothing based on the relative efficiency of price movement". In this indicator: Rather than applying KAMA to price directly, it's applied to the midpoint between the BW Stop and the Slow SuperTrend. This midpoint is a computed halfway value between the two lines. KAMA then smooths that midpoint adaptively, producing `kama_mid`. The fill colors you see on the chart are drawn between kama_mid and bw_stop — not between price and anything else. Dual SuperTrend (Signals and Fill State Logic) "Created by Olivier Seban, SuperTrend combines ATR-based volatility with trend detection into a single line that repositions dynamically as price confirms or breaks the current trend direction." In this indicator: Two SuperTrend lines run simultaneously. The Slow ST (9× ATR) is the macro trend reference. The Fast ST (6× ATR) is never plotted at full size — it's compressed halfway toward the BW Stop and shown as orange circles fast_shortened Putting It All Together The flow through the indicator is linear: Butterworth smooths price → Parkinson sizes the stop → the state machine builds the stop line → CMO colors it → KAMA anchors the midline fill → the dual SuperTrend fires signals and shades conviction. END Every component feeds the next, meaning the final signals and visuals are the product of five sequential filters rather than any single calculation — which is what gives the indicator its resistance to false signals in noisy market conditions.
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của Jamallo22
6
Universal Moving Average🙏🏻 UMA (Universal Moving Average) represents the most natural and prolly ‘the’ final general universal entity for calculating rolling typical value for any type of time-series. Simply via different weighting schemes applied together, it encodes: Location of each datapoint in corresponding fields (price, time, volume) Informational relevance of each datapoint via using windowing functions that are fundamental in nature and go beyond DSP inventions & approximations Innovation in state space (in our case = volatility) The real beauty of this development: being simply a weighting scheme that can be applied to anything: be it weighted median , weighted quantile regression, or weighted KDE , or a simple weighted mean (like in this script). As long as a method accepts weights, you can harness the power of this entity. It means that final algorithmic complexity will match your initial tool. As a moving ‘average’ it beats ALMA, KAMA, MAMA, VIDYA and all others because it is a simple and general entity, and all it does is encoding ‘all’ available information. I think that post might anger a lot of people, because lotta things will be realized as legacy and many paywalls gonna be ignored, specially for the followers of DSP cult, the ones who yet don’t understand that aggregated tick data is not a signal omg, it’s a completely different type of time series where your methods simply don’t fit even closely. I am also sorry to inform y’all, that spectral analysis is much closer to state-space methods in spirit than to DSP. But in fact DSP is cool and I love it, well for actual signals xD ... Weights explained & how to use them: as I already said, the whole thing is based on combining different set of weights, and you can turn them on/off in script settings. Btw I've set em up defaults so you can use the thing on price data out of the box right away. Price, Time, Volume weights: encode location of every datapoint in Price & TIme & Volume field Howtouse: u have to disable one weight that corresponds to the field you apply UMA to. E.g if you apply UMA to prices, you turn off price weighting And turn on time and volume weighting. Or if you apply UMA to volume delta, you turn off volume weighting And turn on price and time weighting. Higher prices are more important, this asymmetry is confirmed and even proved by the fact that prices can’t be negative (don’t even mention that incorrect rollover on CL contract in 2k20...). Signal weights: encode actuality/importance/relevance of datapoints. Howtouse: in DSP terms, it provides smoothing, but also compensates for the lag it introduces. This smoothness is useful if you use slope reversals for signal generation aka watching peaks and valleys in a moving average shape. It's also better to perturb smoothed outputs with this , this way you inject high freq content back, But in controlled way! Signal = information. The fundamental universal entity behind so-called “smoothing” in DSP has nothing to do with signals and goes eons beyond DSP. This is simply about measuring the relevance of data in time. First, new datapoints need some time to be “embedded” into the timeline, you can think of it as time proof, kinda stuff needs time to be proved, accepted; while earliest datapoints lose relevance in time. Second, along with the first notion, at the same time there’s the counter notion that simply weights new data more, acting as a counterweight from the down-weighting of the latest datapoints introduced by the first notion. The first part can be represented as PDF of beta(2, 2) window (a set of weights in our case). It’s actually well known as the Welch window, that lives in between so called statistical and DSP worlds, emerges in multiple contexts. Mainstream DSP users tho mostly don’t use this one, they use primitive legacy windowing function, you can find all kinds on this wiki page. Now the second part, where DSP adepts usually stop, is to introduce the second compensating windowing function. Instead they try to reduce window size, or introduce other kinds of volatility weights, do some tricks, but it ain’t provides obviously. The natural step here is to simply use the integral of the initial window; if the initial window is beta(2, 2) then what we simply need is CDF of beta(2, 2), in fact the vertically inverted shape of it aka survival function . That’s it bros. Simply as that. When both of these are applied you have smth magical, your output becomes smooth and yet not lagging. No arbitrary windowing functions, tricks with data modification etc Why beta(2, 2)? It naturally arises in many contexts, it’s based on one of the most fundamental functions in the universe: x^2. It has finite support. I can talk more bout it on request, but I am absolutely sure this is it. ^^ impulse response of the resulting weighs together (green) compared with uniform weights aka boxcar (red). Made with this script . Weighing by state: encodes state-space innovation of each datapoint, basically magnitude of changes, strength of these changes, aka volatility. Howtouse: this makes your moving average volatility aware in proper math ways. The influence of datapoints will be stronger when changes are stronger. This is weighting by innovations, or weighting by volatility by using squared returns. Why squared returns? They encode state‑space innovations properly because the innovation of any continuous‑time semimartingale is about its quadratic variation, and quadratic variation is built from squared increments, not absolute increments. Adaptive length is not the right way to introduce adaptivity by volatility xD. When you weight datapoints by squared returns you’re already dynamically varying ‘effective’ data size, you don’t need anything else. ... It’s all good, progress happens, that’s how the Universe works, that's how Universal Moving Average works. Time to evolve. I might update other scripts with this complete weighting scheme, either by my own desire or your request. ... ∞
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của gorx1
5
Multivariate Kalman Filter🙏🏻 I see no1 ever posted an open source Multivariate Kalman filter on TV, so here it is, for you. Tested and mathematically correct implementation, with numerical safeties in place that do not affect the final results at all. That’s the main purpose of this drop, just to make the tool available here. Linear algebra everywhere, Neo would approve 4 sure. ... Personally I haven't found any real use case of it for myself, aside from a very specific one I will explain later, but others usually do… Almost every1 in the quant industry who uses Kalman is in fact misusing it, because by its real definition, it should be applied to Not the exact known values (e.g as real ticks provided by transparent audited regulated exchange), but “measurements” of those ‘with errors’. If your measurements don’t have errors or you have real precise data, by its internal formulas Kalman will output the exact inputs. So most who use it come up with some imaginary errors of sorts, like from some kind of imaginary fair price etc. The important easy to miss point, the errors of your measurements have to be symmetric around its mean ‘ at least ’, if errors are biased, Kalman won’t provide. For most tasks there are better tools, including other state space models , but still Multivariate Kalman is a very powerful instrument, you can make it do all kinds of stuff. Also as a state space model it can also provide confidence & prediction intervals without explicit calculations of dem. ... In this script I included 2 example use cases, the first one is the classic tho perfectly working misuse, the second one is what I do with it: One Naive, estimates “hidden” adaptive moving regression endpoint. The result you can see on the chart above. You can imagine that your real datapoints are in fact non perfect measures of some hidden state, and by defining measurement noise and process noise, and by constructing the input matrixes in certain ways, you can express what that state should be. Two Upscaling tick lattice, aka modelling prices as if native tick size would’ve been lower. Kinda very specific task, mostly needed in HFT or just for analytical purposes. Some like ZN have huge tick sizes, they are traded a lot but barely do more than 20 ticks range in a session. The idea is to model raw data as AR2 process , learn the phi1 and phi2, make one point forecasts based on dem, and the process noise would be the variance of errors from these forecasts. The measurement noise here is legit, it’s quantization noise based on tick size, no need in olympic gold in mental gymnastics xd ^^ artificially upscaling ZN futures tick lattice ... I really made it available there so You guys can take it and some crazy ish with it, just let state space models abduct your conciseness and never look back ∞
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của gorx1
2
WLSMA: fast approximation🙏🏻 Sup TV & @alexgrover O(N) algocomplexity, just one loop inside. No, you can't do O(1) @ updates in moving window mode, only expanding window will allow that. Now I have time series & stats models of my own creation, nowhere else available, just TV and my github for now, ain’t no legacy academic industry I always have fun about, but back in 2k20 when I consciously ain’t known much about quant, I remember seeing post by @alexgrover recreating Moving Regression Endpoint dropped on price chart (called LSMA here) as a linear filter combination of filters (yea yeah DSP terms) as 3WMA - 2SMA. Now it’s my time to do smth alike aye? ... This script is remake of my 1st degree WLSMA via linear filter combo. It’s much faster, we aint calculate moving regression per se, we just match its freq response. You can see it on the screen (WLSMAfa) almost perfectly matching the original one (WLSMA). ... While humans like to overfit, I fw generalizations. So your lovely WMA is actually just one case of a more general weight pattern: pow(len - i, e), where pow is the power function and e is the exponent itself. So: - If e = 0, then we have SMA (every number in 0th power is one) - If e = 1, we get WMA - If e = 2, we get quadratic weights. We can recreate WLSMA freq response then by combining 2 filters with e = 1 and e = 2. This is still an approximation, even tho enormously precise for the tasks you’ve shared with me. Due to the non-linear nature of the thing it’s all we can do, and as window size grows, even this small discrepancy converges with true WLSMA value, so we’re all good. Pls don’t try to model this 0.00xxxx discrepancy, it’s not natural. ... DSP approach is unnatural for prices, but you can put this thing on volume delta and be happy, or on other metrics of yours, if for some reason u dont wanna estimate thresholds by fitting a distro. All good TV ∞ P.S.: strangely, the first script made & dropped in the location in Saint P where my actual quant way has started ~5 years ago xD, very thankful
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của gorx1
4
[GYTS] Filters ToolkitFilters Toolkit indicator 🌸 Part of GoemonYae Trading System (GYTS) 🌸 🌸 --------- 1. INTRODUCTION --------- 🌸 💮 Overview The GYTS Filters Toolkit indicator is an advanced, interactive interface built atop the high‐performance, curated functions provided by the FiltersToolkit library . It allows traders to experiment with different combinations of filtering methods -— from smoothing low-pass filters to aggressive detrenders. With this toolkit, you can build custom indicators tailored to your specific trading strategy, whether you're looking for trend following, mean reversion, or cycle identification approaches. 🌸 --------- 2. FILTER METHODS AND TYPES --------- 🌸 💮 Filter categories The available filters fall into four main categories, each marked with a distinct symbol: 🌗 Low Pass Filters (Smoothers) These filters attenuate high-frequency components (noise) while allowing low-frequency components (trends) to pass through. Examples include: Ultimate Smoother Super Smoother (2-pole and 3-pole variants) MESA Adaptive Moving Average (MAMA) and Following Adaptive Moving Average (FAMA) BiQuad Low Pass Filter ADXvma (Adaptive Directional Volatility Moving Average) A2RMA (Adaptive Autonomous Recursive Moving Average) Low pass filters are displayed on the price chart by default, as they follow the overall price movement. If they are combined with a high-pass or bandpass filter, they will be displayed in the subgraph. 🌓 High Pass Filters (Detrenders) These filters do the opposite of low pass filters - they remove low-frequency components (trends) while allowing high-frequency components to pass through. Examples include: Butterworth High Pass Filter BiQuad High Pass Filter High pass filters are displayed as oscillators in the subgraph below the price chart, as they fluctuate around a zero line. 🌑 Band Pass Filters (Cycle Isolators) These filters combine aspects of both low and high pass filters, isolating specific frequency ranges while attenuating both higher and lower frequencies. Examples include: Ehlers Bandpass Filter Cyber Cycle Relative Vigor Index (RVI) BiQuad Bandpass Filter Band pass filters are also displayed as oscillators in a separate panel. 🔮 Predictive Filter Voss Predictive Filter: A special filter that attempts to predict future values of band-limited signals (only to be used as post-filter). Keep its prediction horizon short (1–3 bars) for reasonable accuracy. Note that the the library contains elaborate documentation and source material of each filter. 🌸 --------- 3. INDICATOR FEATURES --------- 🌸 💮 Multi-filter configuration One of the most powerful aspects of this indicator is the ability to configure multiple filters. compare them and observe their combined effects. There are four primary filters, each with its own parameter settings. 💮 Post-filtering Process a filter’s output through an additional filter by enabling the post-filter option. This creates a filter chain where the output of one filter becomes the input to another. Some powerful combinations include: Ultimate Smoother → MAMA: Creates an adaptive smoothing effect that responds well to market changes, good for trend-following strategies Butterworth → Super Smoother → Butterworth: Produces a well-behaved oscillator with minimal phase distortion, John Ehlers also calls a "roofing filter". Great for identifying overbought/oversold conditions with minimal lag. A bandpass filter → Voss Prediction filter: Attempts to predict future movements of cyclical components, handy to find peaks and troughs of the market cycle. 💮 Aggregate filters Arguably the coolest feature: aggregating filters allow you to combine multiple filters with different weights. Important notes about aggregation: You can only aggregate filters that appear on the same chart (price chart or oscillator panel). The weights are automatically normalised, so only their relative values matter Setting a weight to 0 (zero) excludes that filter from the aggregation Filters don't need to be visibly displayed to be included in aggregation 💮 Rich visualisation & alerts The indicator intelligently determines whether a filter is displayed on the price chart or in the subgraph (as an oscillator) based on its characteristics. Dynamic colour palettes, adjustable line widths, transparency, and custom fill between any of enabled filters or between oscillators and the zero-line. A clear legend showing which filters are active and how they're configured Alerts for direction changes and crossovers of all filters 🌸 --------- 4. ACKNOWLEDGEMENTS --------- 🌸 This toolkit builds on the work of numerous pioneers in technical analysis and digital signal processing: John Ehlers, whose groundbreaking research forms the foundation of many filters. Robert Bristow-Johnson for the BiQuad filter formulations. The TradingView community, especially @The_Peaceful_Lizard, @alexgrover, and others mentioned in the code of the library. Everyone who has provided feedback, testing and support!
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của GoemonYae
[GYTS] FiltersToolkit LibraryFiltersToolkit Library 🌸 Part of GoemonYae Trading System (GYTS) 🌸 🌸 --------- 1. INTRODUCTION --------- 🌸 💮 What Does This Library Contain? This library is a curated collection of high-performance digital signal processing (DSP) filters and auxiliary functions designed specifically for financial time series analysis. It includes a shortlist of our favourite and best performing filters — each rigorously tested and selected for their responsiveness, minimal lag and robustness in diverse market conditions. These tools form an integral part of the GoemonYae Trading System (GYTS), chosen for their unique characteristics in handling market data. The library contains two main categories: 1. Smoothing filters (low-pass filters and moving averages) for e.g. denoising, trend following 2. Detrending tools (high-pass and band-pass filters, known as "oscillators") for e.g. mean reversion This collection is finely tuned for practical trading applications and is therefore not meant to be exhaustive. However, will continue to expand as we discover and validate new filtering techniques. I welcome collaboration and suggestions for novel approaches. 🌸 ——— 2. ADDED VALUE ——— 🌸 💮 Unified syntax and comprehensive documentation The FiltersToolkit Library brings together a wide array of valuable filters under a unified, intuitive syntax. Each function is thoroughly documented, with clear explanations and academic sources that underline the mathematical rigour behind the methods. This level of documentation not only facilitates integration into trading strategies but also helps underlying the underlying concepts and rationale. 💮 Optimised performance and readability The code prioritizes computational efficiency while maintaining readability. Key optimizations include: - Minimizing redundant calculations in recursive filters - Smart coefficient caching - Efficient state management - Vectorized operations where applicable 💮 Enhanced functionality and flexibility Some filters in this library introduce extended functionality beyond the original publications. For instance, the MESA Adaptive Moving Average (MAMA) and Ehlers’ Combined Bandpass Filter incorporate multiple variations found in the literature, thereby providing traders with flexible tools that can be fine-tuned to different market conditions. 🌸 ——— 3. THE FILTERS ——— 🌸 💮 Hilbert Transform Function This function implements the Hilbert Transform as utilised by John Ehlers. It converts a real-valued time series into its analytic signal, enabling the extraction of instantaneous phase and frequency information—an essential step in adaptive filtering. Source: John Ehlers - "Rocket Science for Traders" (2001), "TASC 2001 V. 19:9", "Cybernetic Analysis for Stocks and Futures" (2004) 💮 Homodyne Discriminator By leveraging the Hilbert Transform, this function computes the dominant cycle period through a Homodyne Discriminator. It extracts the in-phase and quadrature components of the signal, facilitating a robust estimation of the underlying cycle characteristics. Source: John Ehlers - "Rocket Science for Traders" (2001), "TASC 2001 V. 19:9", "Cybernetic Analysis for Stocks and Futures" (2004) 💮 MESA Adaptive Moving Average (MAMA) An advanced dual-stage adaptive moving average, this function outputs both the MAMA and its companion FAMA. It combines adaptive alpha computation with elements from Kaufman’s Adaptive Moving Average (KAMA) to provide a responsive and reliable trend indicator. Source: John Ehlers - "Rocket Science for Traders" (2001), "TASC 2001 V. 19:9", "Cybernetic Analysis for Stocks and Futures" (2004) 💮 BiQuad Filters A family of second-order recursive filters offering exceptional control over frequency response: - High-pass filter for detrending - Low-pass filter for smooth trend following - Band-pass filter for cycle isolation The quality factor (Q) parameter allows fine-tuning of the resonance characteristics, making these filters highly adaptable to different market conditions. Source: Robert Bristow-Johnson's Audio EQ Cookbook, implemented by @The_Peaceful_Lizard 💮 Relative Vigor Index (RVI) This filter evaluates the strength of a trend by comparing the closing price to the trading range. Operating similarly to a band-pass filter, the RVI provides insights into market momentum and potential reversals. Source: John Ehlers – “Cybernetic Analysis for Stocks and Futures” (2004) 💮 Cyber Cycle The Cyber Cycle filter emphasises market cycles by smoothing out noise and highlighting the dominant cyclical behaviour. It is particularly useful for detecting trend reversals and cyclical patterns in the price data. Source: John Ehlers – “Cybernetic Analysis for Stocks and Futures” (2004) 💮 Butterworth High Pass Filter Inspired by the classical Butterworth design, this filter achieves a maximally flat magnitude response in the passband while effectively removing low-frequency trends. Its design minimises phase distortion, which is vital for accurate signal interpretation. Source: John Ehlers – “Cybernetic Analysis for Stocks and Futures” (2004) 💮 2-Pole SuperSmoother Employing a two-pole design, the SuperSmoother filter reduces high-frequency noise with minimal lag. It is engineered to preserve trend integrity while offering a smooth output even in noisy market conditions. Source: John Ehlers – “Cybernetic Analysis for Stocks and Futures” (2004) 💮 3-Pole SuperSmoother An extension of the 2-pole design, the 3-pole SuperSmoother further attenuates high-frequency noise. Its additional pole delivers enhanced smoothing at the cost of slightly increased lag. Source: John Ehlers – “Cybernetic Analysis for Stocks and Futures” (2004) 💮 Adaptive Directional Volatility Moving Average (ADXVma) This adaptive moving average adjusts its smoothing factor based on directional volatility. By combining true range and directional movement measurements, it remains exceptionally flat during ranging markets and responsive during directional moves. Source: Various implementations across platforms, unified and optimized 💮 Ehlers Combined Bandpass Filter with Automated Gain Control (AGC) This sophisticated filter merges a highpass pre-processing stage with a bandpass filter. An integrated Automated Gain Control normalises the output to a consistent range, while offering both regular and truncated recursive formulations to manage lag. Source: John F. Ehlers – “Truncated Indicators” (2020), “Cycle Analytics for Traders” (2013) 💮 Voss Predictive Filter A forward-looking filter that predicts future values of a band-limited signal in real time. By utilising multiple time-delayed feedback terms, it provides anticipatory coupling and delivers a short-term predictive signal. Source: John Ehlers - "A Peek Into The Future" (TASC 2019-08) 💮 Adaptive Autonomous Recursive Moving Average (A2RMA) This filter dynamically adjusts its smoothing through an adaptive mechanism based on an efficiency ratio and a dynamic threshold. A double application of an adaptive moving average ensures both responsiveness and stability in volatile and ranging markets alike. Very flat response when properly tuned. Source: @alexgrover (2019) 💮 Ultimate Smoother (2-Pole) The Ultimate Smoother filter is engineered to achieve near-zero lag in its passband by subtracting a high-pass response from an all-pass response. This creates a filter that maintains signal fidelity at low frequencies while effectively filtering higher frequencies at the expense of slight overshooting. Source: John Ehlers - TASC 2024-04 "The Ultimate Smoother" Note: This library is actively maintained and enhanced. Suggestions for additional filters or improvements are welcome through the usual channels. The source code contains a list of tested filters that did not make it into the curated collection.
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của GoemonYae
14
PaddingThe Padding library is a comprehensive and flexible toolkit designed to extend time series data within TradingView, making it an indispensable resource for advanced signal processing tasks such as FFT, filtering, convolution, and wavelet analysis. At its core, the library addresses the common challenge of edge effects by "padding" your data—that is, by appending additional data points beyond the natural boundaries of your original dataset. This extension not only mitigates the distortions that can occur at the endpoints but also helps to maintain the integrity of various transformations and calculations performed on the series. The library accomplishes this while preserving the ordering of your data, ensuring that the most recent point always resides at index 0. Central to the functionality of this library are two key enumerations: Direction and PaddingType. The Direction enum determines where the padding will be applied. You can choose to extend the data in the forward direction (ahead of the current values), in the backward direction (behind the current values), or in both directions simultaneously. The PaddingType enum defines the specific method used for extending the data. The library supports several methods—including symmetric, reflect, periodic, antisymmetric, antireflect, smooth, constant, and zero padding—each of which has been implemented to suit different analytical scenarios. For instance, symmetric padding mirrors the original data across its boundaries, while reflect padding continues the trend by reflecting around endpoint values. Periodic padding repeats the data, and antisymmetric padding mirrors the data with alternating signs to counterbalance it. The antireflect and smooth methods take into account the derivatives of your data, thereby extending the series in a way that preserves or smoothly continues these derivative values. Constant and zero padding simply extend the series using fixed endpoint values or zeros. Together, these enums allow you to fine-tune how your data is extended, ensuring that the padding method aligns with the specific requirements of your analysis. The library is designed to work with both single variable inputs and array inputs. When using array-based methods—particularly with the antireflect and smooth padding types—please note that the implementation intentionally discards the last data point as a result of the delta computation process. This behavior is an important consideration when integrating the library into your TradingView studies, as it affects the overall data length of the padded series. Despite this, the library’s structure and documentation make it straightforward to incorporate into your existing scripts. You simply provide your data source, define the length of your data window, and select the desired padding type and direction, along with any optional parameters to control the extent of the padding (using both_period, forward_period, or backward_period). In practical application, the Padding library enables you to extend historical data beyond its original range in a controlled and predictable manner. This is particularly useful when preparing datasets for further signal processing, as it helps to reduce artifacts that can otherwise compromise the results of your analytical routines. Whether you are an experienced Pine Script developer or a trader exploring advanced data analysis techniques, this library offers a robust solution that enhances the reliability and accuracy of your studies by ensuring your algorithms operate on a more complete and well-prepared dataset. Library "Padding" A comprehensive library for padding time series data with various methods. Supports both single variable and array inputs, with flexible padding directions and periods. Designed for signal processing applications including FFT, filtering, convolution, and wavelets. All methods maintain data ordering with most recent point at index 0. symmetric(source, series_length, direction, both_period, forward_period, backward_period)   Applies symmetric padding by mirroring the input data across boundaries   Parameters:      source (float) : Input value to pad from      series_length (int) : Length of the data window      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with symmetric padding applied method symmetric(source, direction, both_period, forward_period, backward_period)   Applies symmetric padding to an array by mirroring the data across boundaries   Namespace types: array   Parameters:      source (array) : Array of values to pad      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with symmetric padding applied reflect(source, series_length, direction, both_period, forward_period, backward_period)   Applies reflect padding by continuing trends through reflection around endpoint values   Parameters:      source (float) : Input value to pad from      series_length (int) : Length of the data window      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with reflect padding applied method reflect(source, direction, both_period, forward_period, backward_period)   Applies reflect padding to an array by continuing trends through reflection around endpoint values   Namespace types: array   Parameters:      source (array) : Array of values to pad      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with reflect padding applied periodic(source, series_length, direction, both_period, forward_period, backward_period)   Applies periodic padding by repeating the input data   Parameters:      source (float) : Input value to pad from      series_length (int) : Length of the data window      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with periodic padding applied method periodic(source, direction, both_period, forward_period, backward_period)   Applies periodic padding to an array by repeating the data   Namespace types: array   Parameters:      source (array) : Array of values to pad      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with periodic padding applied antisymmetric(source, series_length, direction, both_period, forward_period, backward_period)   Applies antisymmetric padding by mirroring data and alternating signs   Parameters:      source (float) : Input value to pad from      series_length (int) : Length of the data window      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with antisymmetric padding applied method antisymmetric(source, direction, both_period, forward_period, backward_period)   Applies antisymmetric padding to an array by mirroring data and alternating signs   Namespace types: array   Parameters:      source (array) : Array of values to pad      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with antisymmetric padding applied antireflect(source, series_length, direction, both_period, forward_period, backward_period)   Applies antireflect padding by reflecting around endpoints while preserving derivatives   Parameters:      source (float) : Input value to pad from      series_length (int) : Length of the data window      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with antireflect padding applied method antireflect(source, direction, both_period, forward_period, backward_period)   Applies antireflect padding to an array by reflecting around endpoints while preserving derivatives   Namespace types: array   Parameters:      source (array) : Array of values to pad      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with antireflect padding applied. Note: Last data point is lost when using array input smooth(source, series_length, direction, both_period, forward_period, backward_period)   Applies smooth padding by extending with constant derivatives from endpoints   Parameters:      source (float) : Input value to pad from      series_length (int) : Length of the data window      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with smooth padding applied method smooth(source, direction, both_period, forward_period, backward_period)   Applies smooth padding to an array by extending with constant derivatives from endpoints   Namespace types: array   Parameters:      source (array) : Array of values to pad      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with smooth padding applied. Note: Last data point is lost when using array input constant(source, series_length, direction, both_period, forward_period, backward_period)   Applies constant padding by extending endpoint values   Parameters:      source (float) : Input value to pad from      series_length (int) : Length of the data window      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with constant padding applied method constant(source, direction, both_period, forward_period, backward_period)   Applies constant padding to an array by extending endpoint values   Namespace types: array   Parameters:      source (array) : Array of values to pad      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with constant padding applied zero(source, series_length, direction, both_period, forward_period, backward_period)   Applies zero padding by extending with zeros   Parameters:      source (float) : Input value to pad from      series_length (int) : Length of the data window      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with zero padding applied method zero(source, direction, both_period, forward_period, backward_period)   Applies zero padding to an array by extending with zeros   Namespace types: array   Parameters:      source (array) : Array of values to pad      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with zero padding applied pad_data(source, series_length, padding_type, direction, both_period, forward_period, backward_period)   Generic padding function that applies specified padding type to input data   Parameters:      source (float) : Input value to pad from      series_length (int) : Length of the data window      padding_type (series PaddingType) : Type of padding to apply (see PaddingType enum)      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with specified padding applied method pad_data(source, padding_type, direction, both_period, forward_period, backward_period)   Generic padding function that applies specified padding type to array input   Namespace types: array   Parameters:      source (array) : Array of values to pad      padding_type (series PaddingType) : Type of padding to apply (see PaddingType enum)      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to array length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to array length if not specified   Returns: Array ordered with most recent point at index 0, containing original data with specified padding applied. Note: Last data point is lost when using antireflect or smooth padding types make_padded_data(source, series_length, padding_type, direction, both_period, forward_period, backward_period)   Creates a window-based padded data series that updates with each new value. WARNING: Function must be called on every bar for consistency. Do not use in scopes where it may not execute on every bar.   Parameters:      source (float) : Input value to pad from      series_length (int) : Length of the data window      padding_type (series PaddingType) : Type of padding to apply (see PaddingType enum)      direction (series Direction) : Direction to apply padding      both_period (int) : Optional - periods to pad in both directions. Overrides forward_period and backward_period if specified      forward_period (int) : Optional - periods to pad forward. Defaults to series_length if not specified      backward_period (int) : Optional - periods to pad backward. Defaults to series_length if not specified   Returns: Array ordered with most recent point at index 0, containing windowed data with specified padding applied
Thư viện
của The_Peaceful_Lizard
6 Band Parametric EQThis indicator implements a complete parametric equalizer on any data source using high-pass and low-pass filters, high and low shelving filters, and six fully configurable bell filters. Each filter stage features standard audio DSP controls including frequency, Q factor, and gain where applicable. While parametric EQ is typically used for audio processing, this implementation raises questions about the nature of filtering in technical analysis. Why stop at simple moving averages when you can shape your signal's frequency response with surgical precision? The answer may reveal more about our assumptions than our indicators. Filter Types and Parameters High-Pass Filter: A high-pass filter attenuates frequency components below its cutoff frequency while passing higher frequencies. The Q parameter controls resonance at the cutoff point, with higher values creating more pronounced peaks. Low-Pass Filter: The low-pass filter does the opposite - it attenuates frequencies above the cutoff while passing lower frequencies. Like the high-pass, its Q parameter affects the resonance at the cutoff frequency. High/Low Shelf Filters: Shelf filters boost or cut all frequencies above (high shelf) or below (low shelf) the target frequency. The slope parameter determines the steepness of the transition around the target frequency , with a value of 1.0 creating a gentle slope and lower values making the transition more abrupt. The gain parameter sets the amount of boost or cut in decibels. Bell Filters: Bell (or peaking) filters create a boost or cut centered around a specific frequency. A bell filter's frequency parameter determines the center point of the effect, while Q controls the width of the affected frequency range - higher Q values create a narrower bandwidth. The gain parameter defines the amount of boost or cut in decibels. All filters run in series, processing the signal in this order: high-pass → low shelf → bell filters → high shelf → low-pass. Each stage can be independently enabled or bypassed. The frequency parameter for all filters represents the period length of the targeted frequency component. Lower values target higher frequencies and vice versa. All gain values are in decibels, where positive values boost and negative values cut. The 6-Band Parametric EQ combines these filters into a comprehensive frequency shaping tool. Just as audio engineers use parametric EQs to sculpt sound, this indicator lets you shape market data's frequency components with surgical precision. But beyond its technical implementation, this indicator serves as a thought experiment about the nature of filtering in technical analysis. While traditional indicators often rely on simple moving averages or single-frequency filters, the parametric EQ takes this concept to its logical extreme - offering complete control over the frequency domain of price action. Whether this level of filtering precision is useful for analysis is perhaps less important than what it reveals about our assumptions regarding market data and its frequency components.
Chỉ báo
của The_Peaceful_Lizard
6
FIR Low Pass Filter Suite (FIR)The FIR Low Pass Filter Suite is an advanced signal processing indicator that applies finite impulse response (FIR) filtering techniques to price data. At its core, the indicator uses windowed-sinc filtering, which provides optimal frequency response characteristics for separating trend from noise in financial data. The indicator offers multiple window functions including Kaiser, Kaiser-Bessel Derived (KBD), Hann, Hamming, Blackman, Triangular, and Lanczos. Each window type provides different trade-offs between main-lobe width and side-lobe attenuation, allowing users to fine-tune the frequency response characteristics of the filter. The Kaiser and KBD windows provide additional control through an alpha parameter that adjusts the shape of the window function. A key feature is the ability to operate in either linear or logarithmic space. Logarithmic filtering can be particularly appropriate for financial data due to the multiplicative nature of price movements. The indicator includes an envelope system that can adaptively calculate bands around the filtered price using either arithmetic or geometric deviation, with separate controls for upper and lower bands to account for the asymmetric nature of market movements. The implementation handles edge effects through proper initialization and offers both centered and forward-only filtering modes. Centered mode provides zero phase distortion but introduces lag, while forward-only mode operates causally with no lag but introduces some phase distortion. All calculations are performed using vectorized operations for efficiency, with carefully designed state management to handle the filter's warm-up period. Visual feedback is provided through customizable color gradients that can reflect the current trend direction, with optional glow effects and background fills to enhance visibility. The indicator maintains high numerical precision throughout its calculations while providing smooth, artifact-free output suitable for both analysis and visualization.
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của The_Peaceful_Lizard
2
Lanczos CandlesThis indicator reconstructs price action using Lanczos resampling, incorporating lower timeframe data to create a more detailed representation of market movements. Traditional candle aggregation on higher timeframes tends to lose some price action detail - this indicator attempts to preserve more of that information through mathematical resampling. The indicator samples price data from a lower timeframe and uses the Lanczos algorithm, a mathematical method commonly used in signal processing and image resampling, to reconstruct the price series at the chart's timeframe. The process helps maintain price movements that might otherwise be smoothed out in regular candle aggregation. The main settings allow you to select the source timeframe for sampling, adjust the Lanczos filter width to balance smoothness versus detail preservation, and optionally enable Heikin Ashi calculation. The filter width parameter (default: 3) affects how aggressive the smoothing is - higher values produce smoother results while lower values retain more of the original variation. This approach can be useful for technical analysis when you want to work with higher timeframes while maintaining awareness of significant price movements that occurred within those candles. The optional Heikin Ashi mode can help visualize trends in the resampled data. The indicator works best when there's a clear ratio between your chart timeframe and the source timeframe (for example, using 1-minute data to build 5-minute candles).
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của The_Peaceful_Lizard
8
Sinc MAKaiser Windowed Sinc Moving Average Indicator The Kaiser Windowed Sinc Moving Average is an advanced technical indicator that combines the sinc function with the Kaiser window to create a highly customizable finite impulse response (FIR) filter for financial time series analysis. Sinc Function: The Ideal Low-Pass Filter At the core of this indicator is the sinc function, which represents the impulse response of an ideal low-pass filter. In signal processing and technical analysis, the sinc function is crucial because it allows for the creation of filters with precise frequency cutoff characteristics. When applied to financial data, this means the ability to separate long-term trends from short-term fluctuations with remarkable accuracy. The primary advantage of using a sinc-based filter is the independent control over two critical parameters: the cutoff frequency and the number of samples used. The cutoff frequency, analogous to the "length" in traditional moving averages, determines which price movements are considered significant (low frequency) and which are treated as noise (high frequency). By adjusting the cutoff, analysts can fine-tune the filter to respond to specific market cycles or timeframes of interest. The number of samples used in the filter doesn't affect the cutoff frequency but instead influences the filter's accuracy and steepness. Increasing the sample size results in a better approximation of the ideal low-pass filter, leading to sharper transitions between passed and attenuated frequencies. This allows for more precise trend identification and noise reduction without changing the fundamental frequency response characteristics. Kaiser Window: Optimizing the Sinc Filter While the sinc function provides excellent frequency domain characteristics, it has infinite length in the time domain, which is impractical for real-world applications. This is where the Kaiser window comes into play. By applying the Kaiser window to the sinc function, we create a finite-length filter that approximates the ideal response while minimizing unwanted oscillations (known as the Gibbs phenomenon) in the frequency domain. The Kaiser window introduces an additional parameter, alpha, which controls the trade-off between the main-lobe width and side-lobe levels in the frequency response. This parameter allows users to fine-tune the filter's behavior, balancing between sharp cutoffs and minimal ripple effects. Customizable Parameters The Kaiser Windowed Sinc Moving Average offers several key parameters for customization: Cutoff: Controls the filter's cutoff frequency, determining the divide between trends and noise. Length: Sets the number of samples used in the FIR filter calculation, affecting the filter's accuracy and computational complexity. Alpha: Influences the shape of the Kaiser window, allowing for fine-tuning of the filter's frequency response characteristics. Centered and Non-Centered Modes The indicator provides two operational modes: Non-Centered (Real-time) Mode: Uses half of the windowed sinc function, suitable for real-time analysis and current market conditions. Centered Mode: Utilizes the full windowed sinc function, resulting in a zero-phase filter. This mode introduces a delay but offers the most accurate trend identification for historical analysis. Visualization Features To enhance the analytical value of the indicator, several visualization options are included: Gradient Coloring: Offers a range of color schemes to represent trend direction and strength. Glow Effect: An optional visual enhancement for improved line visibility. Background Fill: Highlights the area between the moving average and price, aiding in trend visualization. Applications in Technical Analysis The Kaiser Windowed Sinc Moving Average is particularly useful for precise trend identification, cycle analysis, and noise reduction in financial time series. Its ability to create custom low-pass filters with independent control over cutoff and filter accuracy makes it a powerful tool for analyzing various market conditions and timeframes. Compared to traditional moving averages, this indicator offers superior frequency response characteristics and reduced lag in trend identification when properly tuned. It provides greater flexibility in filter design, allowing analysts to create moving averages tailored to specific trading strategies or market behaviors. Conclusion The Kaiser Windowed Sinc Moving Average represents an advanced approach to price smoothing and trend identification in technical analysis. By making the ideal low-pass filter characteristics of the sinc function practically applicable through Kaiser windowing, this indicator provides traders and analysts with a sophisticated tool for examining price trends and cycles. Its implementation in Pine Script contributes to the TradingView community by making advanced signal processing techniques accessible for experimentation and further development in technical analysis. This indicator serves not only as a practical tool for market analysis but also as an educational resource for those interested in the intersection of signal processing and financial markets. Related script:
Chỉ báo
của The_Peaceful_Lizard
5
Ehlers Band-Pass FilterHeyo, This indicator is an original translation from Ehlers' book "Cycle Analytics for Traders Advanced". First, I describe the indicator as usual and later you can find a very insightful quote of the book. Key Features Signal Line: Represents the output of the band-pass filter, highlighting the dominant cycle in the data. Trigger Line: A leading indicator derived from the signal line, providing early signals for potential market reversals. Dominant Cycle: Measures the dominant cycle period by counting the number of bars between zero crossings of the band-pass filter output. Calculation: The band-pass filter is implemented using a combination of high-pass and low-pass filters. The filter's parameters, such as period and bandwidth, can be adjusted to tune the filter to specific market cycles. The signal line is normalized using an Automatic Gain Control (AGC) to provide consistent amplitude regardless of price swings. The trigger line is derived by applying a high-pass filter to the signal line, creating a leading waveform. Usage The indicator is effective in identifying peaks and valleys in the market data. It works best in cyclic market conditions and may produce false signals during trending periods. The dominant cycle measurement helps traders understand the prevailing market cycle length, aiding in better decision-making. Quoted from the Book Band-Pass Filters “A little of the data narrowly passed,” said Tom broadly. Perhaps the least appreciated and most underutilized filter in technical analysis is the band-pass filter. The band-pass filter simultaneously diminishes the amplitude at low frequencies, qualifying it as a detrender, and diminishes the amplitude at high frequencies, qualifying it as a data smoother. It passes only those frequency components from input to output in which the trader is interested. The filtering produced by a band-pass filter is superior because the rejection in the stop bands is related to its bandwidth. The degree of rejection of undesired frequency components is called selectivity. The band-stop filter is the dual of the band-pass filter. It rejects a band of frequency components as a notch at the output and passes all other frequency components virtually unattenuated. Since the bandwidth of the deep rejection in the notch is relatively narrow and since the spectrum of market cycles is relatively broad due to systemic noise, the band-stop filter has little application in trading. Measuring the Cycle Period The band-pass filter can be used as a relatively simple measurement of the dominant cycle. A cycle is complete when the waveform crosses zero two times from the last zero crossing. Therefore, each successive zero crossing of the indicator marks a half cycle period. We can establish the dominant cycle period as twice the spacing between successive zero crossings. When we measure the dominant cycle period this way, it is best to widen the pass band of the band-pass filter to avoid distorting the measurement simply due to the selectivity of the filter. Using an input bandwidth of 0.7 produces an octave-wide pass band. For example, if the center period of the filter is 20 and the relative bandwidth is 0.7, the bandwidth is 14. That means the pass band of the filter extends from 13-bar periods to 27-bar periods. That is, roughly an octave exists because the longest period is twice the shortest period of the pass band. It is imperative that a high-pass filter is tuned one octave below the half-bandwidth edge of the band-pass filter to ensure a nominal zero mean of the filtered output. Without a zero mean, the zero crossings can have a substantial error. Since the measurement of the dominant cycle can vary dramatically from zero crossing to zero crossing, the code limits the change between measurements to be no more than 25 percent. While measuring the changing dominant cycle period via zero crossings of the band-pass waveform is easy, it is not necessarily the most accurate method. Best regards, simwai Good Luck with your trading! 🙌
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của simwai
Biquad Band Pass FilterThis indicator utilizes a biquad band pass filter to isolate and highlight a specific frequency band in price data, helping traders focus on price movements within a targeted frequency range. The Length parameter determines the center frequency of the filter, affecting which frequency band is isolated. Adjusting this parameter allows you to focus on different parts of the price movement spectrum. The Bandwidth (BW) controls the width of the frequency band in octaves. It represents the bandwidth between -3 dB frequencies for the band pass filter. A narrower bandwidth results in a more focused filtering effect, isolating a tighter range of frequencies. Key Features of Biquad Filters Biquad filters are a type of digital filter that provides a combination of low-pass, high-pass, band-pass, and notch filtering capabilities. In this implementation, the biquad filter is configured as a band pass filter, which allows frequencies within a specified band to pass while attenuating frequencies outside this band. This is particularly useful in trading to isolate specific price movements, making it easier to detect patterns and trends within a targeted frequency range. Biquad filters are known for their smooth response and minimal phase distortion, making them ideal for technical analysis. The customizable length and bandwidth allow for flexible adaptation to different trading strategies and market conditions. Designed for real-time charting, the biquad filter operates efficiently without significant lag, ensuring timely analysis. By incorporating this biquad band pass filter into your trading toolkit, you can enhance your chart analysis with clearer insights into specific frequency bands of price movements, leading to more informed trading decisions.
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của The_Peaceful_Lizard
5
Biquad High Pass FilterThis indicator utilizes a biquad high pass filter to filter out low-frequency components from price data, helping traders focus on high-frequency movements and detect rapid changes in trends. The Length parameter determines the cutoff frequency of the filter, affecting how quickly the filter responds to changes in price. A shorter length allows the filter to react more quickly to high-frequency movements. The Q Factor controls the sharpness of the filter. A higher Q value results in a more precise filtering effect by narrowing the frequency band. However, be cautious when setting the Q factor too high, as it can induce resonance, amplifying certain frequencies and potentially making the filter less effective by introducing unwanted noise. Key Features of Biquad Filters Biquad filters are a type of digital filter that provides a combination of low-pass, high-pass, band-pass, and notch filtering capabilities. In this implementation, the biquad filter is configured as a high pass filter, which allows high-frequency signals to pass while attenuating lower-frequency components. This is particularly useful in trading to highlight rapid price movements, making it easier to spot short-term trends and patterns. Biquad filters are known for their smooth response and minimal phase distortion, making them ideal for technical analysis. The customizable length and Q factor allow for flexible adaptation to different trading strategies and market conditions. Designed for real-time charting, the biquad filter operates efficiently without significant lag, ensuring timely analysis. By incorporating this biquad high pass filter into your trading toolkit, you can enhance your chart analysis with clearer insights into rapid price movements, leading to more informed trading decisions.
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của The_Peaceful_Lizard
Biquad Low Pass FilterThis indicator utilizes a biquad low pass filter to smooth out price data, helping traders identify trends and reduce noise in their analysis. The Length parameter acts as the length of the moving average, determining the smoothness and responsiveness of the filter. Adjusting this parameter changes how quickly the filter reacts to price changes. The Q Factor controls the sharpness of the filter. A higher Q value results in a narrower frequency band, enhancing the precision of the filter. However, be cautious when setting the Q factor too high, as it can induce resonance, amplifying certain frequencies and potentially making the filter less effective by introducing noise. Key Features of Biquad Filters Biquad filters are a type of digital filter that provides a combination of low-pass, high-pass, band-pass, and notch filtering capabilities. In this implementation, the biquad filter is configured as a low pass filter, which allows low-frequency signals to pass while attenuating higher-frequency noise. This is particularly useful in trading to smooth out price data, making it easier to spot underlying trends and patterns. Biquad filters are known for their smooth response and minimal phase distortion, making them ideal for technical analysis. The customizable length and Q factor allow for flexible adaptation to different trading strategies and market conditions. Designed for real-time charting, the biquad filter operates efficiently without significant lag, ensuring timely analysis. By incorporating this biquad low pass filter into your trading toolkit, you can enhance your chart analysis with clearer insights into price movements, leading to more informed trading decisions.
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của The_Peaceful_Lizard
2
MathTransformLibrary "MathTransform" Auxiliary functions for transforming data using mathematical and statistical methods scaler_zscore(x, lookback_window)   Calculates Z-Score normalization of a series.   Parameters:      x (float) : : floating point series to normalize      lookback_window (int) : : lookback period for calculating mean and standard deviation   Returns: Z-Score normalized series scaler_min_max(x, lookback_window, min_val, max_val, empiric_min, empiric_max, empiric_mid)   Performs Min-Max scaling of a series within a given window, user-defined bounds, and optional midpoint   Parameters:      x (float) : : floating point series to transform      lookback_window (int) : : int : optional lookback window size to consider for scaling.      min_val (float) : : float : minimum value of the scaled range. Default is 0.0.      max_val (float) : : float : maximum value of the scaled range. Default is 1.0.      empiric_min (float) : : float : user-defined minimum value of the input data. This means that the output could exceed the `min_val` bound if there is data in `x` lesser than `empiric_min`. If na, it's calculated from `x` and `lookback_window`.      empiric_max (float) : : float : user-defined maximum value of the input data. This means that the output could exceed the `max_val` bound if there is data in `x` greater than `empiric_max`. If na, it's calculated from `x` and `lookback_window`.      empiric_mid (float) : : float : user-defined midpoint value of the input data. If na, it's calculated from `empiric_min` and `empiric_max`.   Returns: rescaled series log(x, base)   Applies logarithmic transformation to a value, base can be user-defined.   Parameters:      x (float) : : floating point value to transform      base (float) : : logarithmic base, must be greater than 0   Returns: logarithm of the value to the given base, if x <= 0, returns logarithm of 1 to the given base exp(x, base)   Applies exponential transformation to a value, base can be user-defined.   Parameters:      x (float) : : floating point value to transform      base (float) : : base of the exponentiation, must be greater than 0   Returns: the result of raising the base to the power of the value power(x, exponent)   Applies power transformation to a value, exponent can be user-defined.   Parameters:      x (float) : : floating point value to transform      exponent (float) : : exponent for the transformation   Returns: the value raised to the given exponent, preserving the sign of the original value tanh(x, scale)   The hyperbolic tangent is the ratio of the hyperbolic sine and hyperbolic cosine. It limits an output to a range of −1 to 1.   Parameters:      x (float) : : floating point series      scale (float) sigmoid(x, scale, offset)   Applies the sigmoid function to a series.   Parameters:      x (float) : : floating point series to transform      scale (float) : : scaling factor for the sigmoid function      offset (float) : : offset for the sigmoid function   Returns: transformed series using the sigmoid function sigmoid_double(x, scale, offset)   Applies a double sigmoid function to a series, handling positive and negative values differently.   Parameters:      x (float) : : floating point series to transform      scale (float) : : scaling factor for the sigmoid function      offset (float) : : offset for the sigmoid function   Returns: transformed series using the double sigmoid function logistic_decay(a, b, c, t)   Calculates logistic decay based on given parameters.   Parameters:      a (float) : : parameter affecting the steepness of the curve      b (float) : : parameter affecting the direction of the decay      c (float) : : the upper bound of the function's output      t (float) : : time variable   Returns: value of the logistic decay function at time t
Thư viện
của GoemonYae
7
STD-Filtered, Variety FIR Digital Filters w/ ATR Bands [Loxx]STD-Filtered, Variety FIR Digital Filters w/ ATR Bands is a FIR Digital Filter indicator with ATR bands. This indicator contains 12 different digital filters. Some of these have already been covered by indicators that I've recently posted. The difference here is that this indicator has ATR bands, allows for frequency filtering, adds a frequency multiplier, and attempts show causality by lagging price input by 1/2 the period input during final application of weights. Period is restricted to even numbers. The 3 most important parameters are the frequency cutoff, the filter window type and the "causal" parameter. Included filter types: - Hamming - Hanning - Blackman - Blackman Harris - Blackman Nutall - Nutall - Bartlet Zero End Points - Bartlet Hann - Hann - Sine - Lanczos - Flat Top Frequency cutoff can vary between 0 and 0.5. General rule is that the greater the cutoff is the "faster" the filter is, and the smaller the cutoff is the smoother the filter is. You can read more about discrete-time signal processing and some of the windowing functions in this indicator here: Window function Window Functions and Their Applications in Signal Processing What are FIR Filters? In discrete-time signal processing, windowing is a preliminary signal shaping technique, usually applied to improve the appearance and usefulness of a subsequent Discrete Fourier Transform. Several window functions can be defined, based on a constant (rectangular window), B-splines, other polynomials, sinusoids, cosine-sums, adjustable, hybrid, and other types. The windowing operation consists of multipying the given sampled signal by the window function. For trading purposes, these FIR filters act as advanced weighted moving averages. A finite impulse response (FIR) filter is a filter whose impulse response (or response to any finite length input) is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response (IIR) filters, which may have internal feedback and may continue to respond indefinitely (usually decaying). The impulse response (that is, the output in response to a Kronecker delta input) of an Nth-order discrete-time FIR filter lasts exactly {\displaystyle N+1}N+1 samples (from first nonzero element through last nonzero element) before it then settles to zero. FIR filters can be discrete-time or continuous-time, and digital or analog. A FIR filter is (similar to, or) just a weighted moving average filter, where (unlike a typical equally weighted moving average filter) the weights of each delay tap are not constrained to be identical or even of the same sign. By changing various values in the array of weights (the impulse response, or time shifted and sampled version of the same), the frequency response of a FIR filter can be completely changed. An FIR filter simply CONVOLVES the input time series (price data) with its IMPULSE RESPONSE. The impulse response is just a set of weights (or "coefficients") that multiply each data point. Then you just add up all the products and divide by the sum of the weights and that is it; e.g., for a 10-bar SMA you just add up 10 bars of price data (each multiplied by 1) and divide by 10. For a weighted-MA you add up the product of the price data with triangular-number weights and divide by the total weight. What is a Standard Deviation Filter? If price or output or both don't move more than the (standard deviation) * multiplier then the trend stays the previous bar trend. This will appear on the chart as "stepping" of the moving average line. This works similar to Super Trend or Parabolic SAR but is a more naive technique of filtering. Included Bar coloring Loxx's Expanded Source Types Signals Alerts Related indicators STD/C-Filtered, N-Order Power-of-Cosine FIR Filter STD/C-Filtered, Power-of-Cosine FIR Filter STD/C-Filtered, Truncated Taylor Family FIR Filter STD/Clutter-Filtered, Variety FIR Filters STD/Clutter-Filtered, Kaiser Window FIR Digital Filter
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của loxx
3
Goertzel Cycle Period [Loxx]Goertzel Cycle Period is an indicator that uses Goertzel algorithm to extract the cycle period of ticker's price input to then be injected into advanced, adaptive indicators and technical analysis algorithms. The following information is extracted from: "MESA vs Goertzel-DFT, 2003 by Dennis Meyers" Background MESA which stands for Maximum Entropy Spectral Analysis is a widely used mathematical technique designed to find the frequencies present in data. MESA was developed by J.P Burg for his Ph.D dissertation at Stanford University in 1975. The use of the MESA technique for stocks has been written about in many articles and has been popularized as a trading technique by John Ehlers. The Fourier Transform is a mathematical technique named after the famed French mathematician Jean Baptiste Joseph Fourier 1768-1830. In its digital form, namely the discrete-time Fourier Transform (DFT) series, is a widely used mathematical technique to find the frequencies of discrete time sampled data. The use of the DFT has been written about in many articles in this magazine (see references section). Today, both MESA and DFT are widely used in science and engineering in digital signal processing. The application of MESA and Fourier mathematical techniques are prevalent in our everyday life from everything from television to cell phones to wireless internet to satellite communications. MESA Advantages & Disadvantage MESA is a mathematical technique that calculates the frequencies of a time series from the autoregressive coefficients of the time series. We have all heard of regression. The simplest regression is the straight line regression of price against time where price(t) = a+b*t and where a and b are calculated such that the square of the distance between price and the best fit straight line is minimized (also called least squares fitting). With autoregression we attempt to predict tomorrows price by a linear combination of M past prices. One of the major advantages of MESA is that the frequency examined is not constrained to multiples of 1/N (1/N is equal to the DFT frequency spacing and N is equal to the number of sample points). For instance with the DFT and N data points we can only look a frequencies of 1/N, 2/N, Ö.., 0.5. With MESA we can examine any frequency band within that range and any frequency spacing between i/N and (i+1)/N . For example, if we had 100 bars of price data, we might be interested in looking for all cycles between 3 bars per cycle and 30 bars/ cycle only and with a frequency spacing of 0.5 bars/cycle. DFT would examine all bars per cycle of between 2 and 50 with a frequency spacing constrained to 1/100. Another of the major advantages of MESA is that the dominant spectral (frequency) peaks of the price series, if they exist, can be identified with fewer samples than the DFT technique. For instance if we had a 10 bar price period and a high signal to noise ratio we could accurately identify this period with 40 data samples using the MESA technique. This same resolution might take 128 samples for the DFT. One major disadvantage of the MESA technique is that with low signal to noise ratios, that is below 6db (signal amplitude/noise amplitude < 2), the ability of MESA to find the dominant frequency peaks is severely diminished.(see Kay, Ref 10, p 437). With noisy price series this disadvantage can become a real problem. Another disadvantage of MESA is that when the dominant frequencies are found another procedure has to be used to get the amplitude and phases of these found frequencies. This two stage process can make MESA much slower than the DFT and FFT . The FFT stands for Fast Fourier Transform. The Fast Fourier Transform(FFT) is a computationally efficient algorithm which is a designed to rapidly evaluate the DFT. We will show in examples below the comparisons between the DFT & MESA using constructed signals with various noise levels. DFT Advantages and Disadvantages. The mathematical technique called the DFT takes a discrete time series(price) of N equally spaced samples and transforms or converts this time series through a mathematical operation into set of N complex numbers defined in what is called the frequency domain. Why would we what to do that? Well it turns out that we can do all kinds of neat analysis tricks in the frequency domain which are just to hard to do, computationally wise, with the original price series in the time domain. If we make the assumption that the price series we are examining is made up of signals of various frequencies plus noise, than in the frequency domain we can easily filter out the frequencies we have no interest in and minimize the noise in the data. We could then transform the resultant back into the time domain and produce a filtered price series that hopefully would be easier to trade. The advantages of the DFT and itís fast computation algorithm the FFT, are that it is extremely fast in calculating the frequencies of the input price series. In addition it can determine frequency peaks for very noisy price series even when the signal amplitude is less than the noise amplitude. One of the disadvantages of the FFT is that straight line, parabolic trends and edge effects in the price series can distort the frequency spectrum. In addition, end effects in the price series can distort the frequency spectrum. Another disadvantage of the FFT is that it needs a lot more data than MESA for spectral resolution. However this disadvantage has largely been nullified by the speed of today's computers. Goertzel algorithm attempts to resolve these problems... What is the Goertzel algorithm? The Goertzel algorithm is a technique in digital signal processing (DSP) for efficient evaluation of the individual terms of the discrete Fourier transform (DFT). It is useful in certain practical applications, such as recognition of dual-tone multi-frequency signaling (DTMF) tones produced by the push buttons of the keypad of a traditional analog telephone. The algorithm was first described by Gerald Goertzel in 1958. Like the DFT, the Goertzel algorithm analyses one selectable frequency component from a discrete signal. Unlike direct DFT calculations, the Goertzel algorithm applies a single real-valued coefficient at each iteration, using real-valued arithmetic for real-valued input sequences. For covering a full spectrum, the Goertzel algorithm has a higher order of complexity than fast Fourier transform (FFT) algorithms, but for computing a small number of selected frequency components, it is more numerically efficient. The simple structure of the Goertzel algorithm makes it well suited to small processors and embedded applications. The main calculation in the Goertzel algorithm has the form of a digital filter, and for this reason the algorithm is often called a Goertzel filter Where is Goertzel algorithm used? This package contains the advanced mathematical technique called the Goertzel algorithm for discrete Fourier transforms. This mathematical technique is currently used in today's space-age satellite and communication applications and is applied here to stock and futures trading. While the mathematical technique called the Goertzel algorithm is unknown to many, this algorithm is used everyday without even knowing it. When you press a cell phone button have you ever wondered how the telephone company knows what button tone you pushed? The answer is the Goertzel algorithm. This algorithm is built into tiny integrated circuits and immediately detects which of the 12 button tones(frequencies) you pushed. Future Additions: Bartels test for cycle significance, testing output cycles for utility Hodrick Prescott Detrending, smoothing Zero-Lag Regression Detrending, smoothing High-pass or Double WMA filtering of source input price data References: 1. Burg, J. P., ëMaximum Entropy Spectral Analysisî, Ph.D. dissertation, Stanford University, Stanford, CA. May 1975. 2. Kay, Steven M., ìModern Spectral Estimationî, Prentice Hall, 1988 3. Marple, Lawrence S. Jr., ìDigital Spectral Analysis With Applicationsî, Prentice Hall, 1987 4. Press, William H., et al, ìNumerical Receipts in C++: the Art of Scientific Computingî, Cambridge Press, 2002. 5. Oppenheim, A, Schafer, R. and Buck, J., ìDiscrete Time Signal Processingî, Prentice Hall, 1996, pp663-634 6. Proakis, J. and Manolakis, D. ìDigital Signal Processing-Principles, Algorithms and Applicationsî, Prentice Hall, 1996., pp480-481 7. Goertzel, G., ìAn Algorithm for he evaluation of finite trigonometric seriesî American Math Month, Vol 65, 1958 pp34-35.
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của loxx
15
loxxfsrrdspfiltsLibrary "loxxfsrrdspfilts" loxxfsrrdspfilts : FATL, SATL, RFTL, & RSTL Digital Signal Filters fatl(src)   fatl   Parameters:      src : float   Returns: result float rftl(src)   rftl   Parameters:      src : float   Returns: result float satl(src)   satl   Parameters:      src : float   Returns: result float rstl(src)   rstl   Parameters:      src : float   Returns: result float
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FATL, SATL, RFTL, & RSTL Digital Signal Filter Smoother [Loxx]FATL, SATL, RFTL, & RSTL Digital Signal Filter (DSP) Smoother is is a baseline indicator with DSP processed source inputs What are digital indicators: distinctions from standard tools, types of filters. To date, dozens of technical analysis indicators have been developed: trend instruments, oscillators, etc. Most of them use the method of averaging historical data, which is considered crude. But there is another group of tools - digital indicators developed on the basis of mathematical methods of spectral analysis. Their formula allows the trader to filter price noise accurately and exclude occasional surges, making the forecast more effective in comparison with conventional indicators. In this review, you will learn about their distinctions, advantages, types of digital indicators and examples of strategies based on them. Two non-standard strategies based on digital indicators Basic technical analysis indicators built into most platforms are based on mathematical formulas. These formulas are a reflection of market behavior in past periods. In other words, these indicators are built based on patterns that were discovered as a result of statistical analysis, which allows one to predict further trend movement to some extent. But there is also a group of indicators called digital indicators. They are developed using mathematical analysis and are an algorithmic spectral system called ATCF (Adaptive Trend & Cycles Following). In this article, I will tell you more about the components of this system, describe the differences between digital and regular indicators, and give examples of 2 strategies with indicator templates. ATCF - Market Spectrum Analysis Method There is a theory according to which the market is chaotic and unpredictable, i.e. it cannot be accurately analyzed. After all, no one can tell how traders will react to certain news, or whether some large investor will want to play against the market like George Soros did with the Bank of England. But there is another theory: many general market trends are logical, and have a rationale, causes and effects. The economy is undulating, which means it can be described by mathematical methods. Digital indicators are defined as a group of algorithms for assessing the market situation, which are based exclusively on mathematical methods. They differ from standard indicators by the form of analysis display. They display certain values: price, smoothed price, volumes. Many standard indicators are built on the basis of filtering the minute significant price fluctuations with the help of moving averages and their variations. But we can hardly call the MA a good filter, because digital indicators that use spectral filters make it possible to do a more accurate calculation. Simply put, digital indicators are technical analysis tools in which spectral filters are used to filter out price noise instead of moving averages. The display of traditional indicators is lines, areas, and channels. Digital indicators can be displayed both in the form of lines and in digital form (a set of numbers in columns, any data in a text field, etc.). The digital display of the data is more like an additional source of statistics; for trading, a standard visual linear chart view is used. All digital models belong to the category of spectral analysis of the market situation. In conventional technical indicators, price indications are averaged over a fixed period of time, which gives a rather rough result. The use of spectral analysis allows us to increase trading efficiency due to the fact that digital indicators use a statistical data set of past periods, which is converted into a “frequency” of the market (period of fluctuations). Fourier theory provides the following spectral ranging of the trend duration: low frequency range (0-4) - a reflection of a long trend of 2 months or more medium frequency range (5-40) - the trend lasts 10-60 days, thus it is referred to as a correction high frequency range (41-130) - price noise that lasts for several days The ATCF algorithm is built on the basis of spectral analysis and includes a set of indicators created using digital filters. Its consists of indicators and filters: FATL: Built on the basis of a low-frequency digital trend filter SATL: Built on the basis of a low-frequency digital trend filter of a different order RFTL: High frequency trend line RSTL: Low frequency trend line Inclucded: 4 DSP filters Bar coloring Keltner channels with variety ranges and smoothing functions Bollinger bands 40 Smoothing filters 33 souce types Variable channels
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