Sinusoidal — Indicators and Strategies

Bitcoin Market Cap wave model weekly This 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!

Bitcoin wave model 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 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. Related Indicators Fourier Extrapolator of 'Caterpillar' SSA of Price Real-Fast Fourier Transform of Price w/ Linear Regression Fourier Extrapolator of Price w/ Projection Forecast Itakura-Saito Autoregressive Extrapolation of Price Helme-Nikias Weighted Burg AR-SE Extra. of Price ***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.

Periodic Channel This 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