Bitcoin wave model

leoum Updated   
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!
Release Notes:
Updated simplified bands formula.
Less parameters, unified form.
Release Notes:
Updated bitcoin wave model.
I have cut the lower parts of the sinusoidal waves since Bitcoin never wanted to go there.
The lower line is also a logarithmic regression (the power law) function.
Bitcoin is following the path with a great pressision !
Release Notes:
Bitcoin is trying to get out of the bands with its recent jump.
Therefore I need to bring the formula to the perfection level never possible before.
Now, with the variable phase shift it became possible to model all 4 bull runs!
Release Notes:
Resent price advancement makes me adjust the model to better fit both the oldest and the newest data.
Release Notes:
Guided by a meticulous analysis of historical data spanning over 14 years, we developed a concise yet extraordinarily accurate power-law model. This model, with merely three numeric parameters, impeccably captures the timing and amplitude of Bitcoin's price oscillations, aligning seamlessly with both peaks and troughs observed in the data. By artfully blending the damped harmonic oscillator with logarithmic regression, our model equips investors and risk managers with a potent tool for navigating the complexities of the cryptocurrency landscape, informing investment strategies, and enhancing risk management approaches.
Furthermore, we have crafted meticulously defined price range bands that encapsulate Bitcoin's overall price movements within well-defined boundaries. Remarkably, this comprehensive model, relying on a mere six numerical parameters, exhibits remarkable precision in forecasting market tops and bottoms, substantiated by its ability to accurately model the dynamics of the past four bull runs.
Please use it for bitcoin weekly price charts only.
Release Notes:
Another updates that incorporate the earlier cycle concept due to ETF driven bull run.
The phase shift is diminishing faster that expected. The width of the bands should be increased a bit. The model fits 5 previous cycles if counting 2 cycles before the first halving.
Just 7 parameters for the whole chart.
Release Notes:
Another update. There is almost perfect fit for all the data after block height 70 000 (h=1/3).
Updated time shift is now -h^(-1.5). It goes to zero much faster due to much faster learning curve for market participants.
The link to the full article will be published in my x.
Release Notes:
I am constantly updating the script to make it clearer, sharper and simpier.
Please find me on x to find more or search for bitcoinwave genesis page for the whole article.
Release Notes:
Updated halving date estimation
Release Notes:
Corrected the scripto for different time periods (not only for weekly)
Adjusted the estimates for the 4th halving date.
Release Notes:
Cleared the code.
Added the Power Law trend.
Updated the marks with the Block Heights.
Release Notes:
Halving date updated

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