Bitcoin Market Cap wave model weeklyThis Bitcoin Market Cap wave model indicator is rooted in the foundation of my previously developed tool, the : Bitcoin wave model
To derive the Total Market Cap from the Bitcoin wave price model, I employed a straightforward estimation for the Total Market Supply (TMS). This estimation relies on the formula:
TMS <= (1 - 2^(-h)) for any h.This equation holds true for any value of h, which will be elaborated upon shortly. It is important to note that this inequality becomes the equality at the dates of halvings, diverging only slightly during other periods.
Bitcoin wave model is based on the logarithmic regression model and the sinusoidal waves, induced by the halving events.
This chart presents the outcome of an in-depth analysis of the complete set of Bitcoin price data available from October 2009 to August 2023.
The central concept is that the logarithm of the Bitcoin price closely adheres to the logarithmic regression model. If we plot the logarithm of the price against the logarithm of time, it forms a nearly straight line.
The parameters of this model are provided in the script as follows: log(BTCUSD) = 1.48 + 5.44log(h).
The secondary concept involves employing the inherent time unit of Bitcoin instead of days:
'h' denotes a slightly adjusted time measurement intrinsic to the Bitcoin blockchain. It can be approximated as (days since the genesis block) * 0.0007. Precisely, 'h' is defined as follows: h = 0 at the genesis block, h = 1 at the first halving block, and so forth. In general, h = block height / 210,000.
Adjustments are made to account for variations in block creation time.
The third concept revolves around investigating halving waves triggered by supply shock events resulting from the halvings. These halvings occur at regular intervals in Bitcoin's native time 'h'. All halvings transpire when 'h' is an integer. These events induce waves with intervals denoted as h = 1.
Consequently, we can model these waves using a sin(2pih - a) function. The parameter determining the time shift is assessed as 'a = 0.4', aligning with earlier expectations for halving events and their subsequent outcomes.
The fourth concept introduces the notion that the waves gradually diminish in amplitude over the progression of "time h," diminishing at a rate of 0.7^h.
Lastly, we can create bands around the modeled sinusoidal waves. The upper band is derived by multiplying the sine wave by a factor of 3.1*(1-0.16)^h, while the lower band is obtained by dividing the sine wave by the same factor, 3.1*(1-0.16)^h.
The current bandwidth is 2.5x. That means that the upper band is 2.5 times the lower band. These bands are forming an exceptionally narrow predictive channel for Bitcoin. Consequently, a highly accurate estimation of the peak of the next cycle can be derived.
The prediction indicates that the zenith past the fourth halving, expected around the summer of 2025, could result in Total Bitcoin Market Cap ranging between 4B and 5B USD.
The projections to the future works well only for weekly timeframe.
Enjoy the mathematical insights!
Sinusoidal
Bitcoin wave modelBitcoin wave model is based on the logarithmic regression model and the sinusoidal waves, induced by the halving events.
This chart presents the outcome of an in-depth analysis of the complete set of Bitcoin price data available from October 2009 to August 2023.
The central concept is that the logarithm of the Bitcoin price closely adheres to the logarithmic regression model. If we plot the logarithm of the price against the logarithm of time, it forms a nearly straight line.
The parameters of this model are provided in the script as follows: log (BTCUSD) = 1.48 + 5.44log(h).
The secondary concept involves employing the inherent time unit of Bitcoin instead of days:
'h' denotes a slightly adjusted time measurement intrinsic to the Bitcoin blockchain. It can be approximated as (days since the genesis block) * 0.0007. Precisely, 'h' is defined as follows: h = 0 at the genesis block, h = 1 at the first halving block, and so forth. In general, h = block height / 210,000.
Adjustments are made to account for variations in block creation time.
The third concept revolves around investigating halving waves triggered by supply shock events resulting from the halvings. These halvings occur at regular intervals in Bitcoin's native time 'h'. All halvings transpire when 'h' is an integer. These events induce waves with intervals denoted as h = 1.
Consequently, we can model these waves using a sin(2pih - a) function. The parameter determining the time shift is assessed as 'a = 0.4', aligning with earlier expectations for halving events and their subsequent outcomes.
The fourth concept introduces the notion that the waves gradually diminish in amplitude over the progression of "time h," diminishing at a rate of 0.7^h.
Lastly, we can create bands around the modeled sinusoidal waves. The upper band is derived by multiplying the sine wave by a factor of 3.1*(1-0.16)^h, while the lower band is obtained by dividing the sine wave by the same factor, 3.1*(1-0.16)^h.
The current bandwidth is 2.5x. That means that the upper band is 2.5 times the lower band. These bands are forming an exceptionally narrow predictive channel for Bitcoin. Consequently, a highly accurate estimation of the peak of the next cycle can be derived.
The prediction indicates that the zenith past the fourth halving, expected around the summer of 2025, could result in prices ranging between 200,000 and 240,000 USD.
Enjoy the mathematical insights!
Fourier Spectrometer of Price w/ Extrapolation Forecast [Loxx]Fourier Spectrometer of Price w/ Extrapolation Forecast is a forecasting indicator that forecasts the sinusoidal frequency of input price. This method uses Linear Regression with a Fast Fourier Transform function for the forecast and is different from previous forecasting methods I've posted. Dotted lines are the forecast frequencies. You can change the UI colors and line widths. This comes with 8 frequencies out of the box. Instead of drawing sinusoidal manually on your charts, you can use this instead. This will render better results than eyeballing the Sine Wave that folks use for trading. this is the real math that automates that process.
Each signal line can be shown as a linear superposition of periodic (sinusoidal) components with different periods (frequencies) and amplitudes. Roughly, the indicator shows those components. It strongly depends on the probing window and changes (recalculates) after each tick; e.g., you can see the set of frequencies showing whether the signal is fast or slow-changing, etc. Sometimes only a small number of leading / strongest components (e.g., 3) can extrapolate the signal quite well.
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***The period parameter doesn't correspond to how many bars back the drawing begins. Lines re rendered according to skipping mechanism due to TradingView limitations.
Composite Synchronous Sinusoidal Harmonics Waveform GeneratorWait, "Composite Synchronous Sinusoidal Harmonics Waveform Generator", say what?? What on earth is that, and what function does this script perform? Keep reading and discover! It's intended and provided freely to use for any TV member at any skill level, not just at the engineering level. This is also available for anyone becoming fluent with why stocks/markets fluctuated the way that they do.
Don't let the entitled name frighten you, it's actually surprisingly fun to just fiddle with. This is ALSO a ingenious PSv4 tinker toy. Change any input() and see how one subtle settings alteration dramatically changes the entire fractal. You might learn something new about this giant financial game we all are determined to play anyways. Double and triple tops, head and shoulders, bounces, cup/handle, consolidations, and MANY-MANY other things are revealed on how they come to exist and why. Funny thing is, this is occurring in minds of traders psychologically. You, me, everyone! Ponder that.
Initially, I wanted a synthetic signal "generator", where I would know for certain what the specific "composing" frequencies are for testing, spectral analysis, filtering, and pattern recognition purposes. Inherent "harmonics" affect nearly every algorithmic indicator you have seen or that may come to exist. While encountering a plethora of cycles, you may see exactly how well your indicators/filters perform when "sourced" to this script with `src = input(close, "Source", input.source)`. Keep in mind, open, high, low, and volume variables are NOT available, if they are employed in your indicators calculations. Feel free to tether this to TV built-in indicators or create your own in TV's Pine Editor, if a source input() isn't already provided. See what happens...
Educating you informatively further, there are "synchronous" irregular harmonic frequencies just like this that do in fact exist in tickers everywhere. While this script's specific generated "sinusoidals" are completely stationary, the ones you will see in REAL price action are ephemeral, emerging and disappearing at any time unexpectedly. The remarkable thing about my creation is, you may notice patterns in the generated fundamental "waveform" that are eerily similar to actual stock market fractal patterns encountered everyday. On just spontaneous random chance, I found a recognizable pattern on a watch list asset displayed above, without looking for it before publishing this. I did not cherry pick that or tune the settings to it. I just bumped up the chart interval one notch and offset the waveform quickly.
As you can witness looking closer, there are numerous pure sine waves artificially created with different amplitudes and phase shifts to form unique patterns that combine together in most unique ways appearing fractal in nature. The sine waves are not derived from any ticker price/volume that you maybe viewing, and should look similar on any time frame chosen. Don't worry about chart intervals. The combination of these with simple addition results in the most unique of waveforms in white. You will notice "dominant cycles", as Dr. John Ehlers would describe them, are the prevailers in movement. Yet those smaller cycles have enormous influence over more powerful cycles and ultimately our indicators.
One intention not included at initial release is a preset waveforms input() to instantly generate very specific patterns, such as a pseudo-square wave, sawtooth wave, and many others that may have applications in real world pattern matching. If you happen to come across very unique ones, you may inform me privately via TV chat and I will consider your gracious considerations of discovered settings for inclusion. I'm awaiting Pine arrays to arrive for that major revision. Yes, you have read that correctly. They have been in the TV contributor/developer oven for quite some time. This was revealed in a "public" announcement recently, and I decided to provide you with a "Get Ready Notification" in this script's description, wink-wink. Pine Script endowed with arrays may be used to create and test spectral decomposition analytics code, filters, or what ever else your mind can surmise utilizing this nifty generator script. You now have another tool for your TV tool belt, to aid with spawning the future evolution of indicators on TradingView. Let the tinkering commence...
Features List Includes:
Waveform offset
Nyquist noise injection
Sine wave enable/disable for all sine waves
Cycle period for all sine waves
Amplitude for all sine waves
Phase shift for all sine waves
The comments section below is solely just for commenting and other remarks, ideas, compliments, etc... regarding only this indicator, not others. When available time provides itself, I will consider your inquiries, thoughts, and concepts presented below in the comments section if you do have any questions or comments regarding this indicator. When my indicators achieve more prevalent use by TV members , I may implement more ideas when they present themselves as worthy additions. As always, "Like" it if you simply just like it with a proper thumbs up, and also return to my scripts list occasionally for additional postings. Have a profitable future everyone!
Periodic ChannelThis indicator try to create a channel by summing a re-scaled and readapted sinusoidal wave form to the price mean.
The length parameter control the speed of the sinusoidal wave form, this parameter is not converted to a sine wave period for allowing a better estimation, higher length's work better but feel free to try shorter periods.
The invert parameter invert the sinusoidal wave.
Each bands represent possible return points, the higher the band the higher the probability.
Inverted sin wave exemple
The performance of the indicator is subjective to the main estimation (blue line), select the parameter that best fit the blue line to the price.
Best ragards
