BTC Power Law Spirals by G. Santostasi

1 thg 3, 2024

This script is based on G. Santostasi's Power Law Spiral Clock.
The Power Law Clock is a projection in polar coordinates of the Power Law Model of BTC price normalized to its natural periodicity of 4 years.

The Power Law model is derived by fitting the price of BTC in a log-log chart assuming that it has a long-term Polar Law Behavior. Using regression it is possible to extract the slope n (that is also the power of the power law) and the y-intercept. These parameters can be used to define a Power Law spiral of the form rho=A*theta^n, where theta is the time in days from the Genesis block normalized to the 4-year cycle.

The script represents 2 models the simple Power Law Spiral as defined above and a more full model with 3 components:
1) A power law trend that is adjusted to 2 standard deviations from the median Power Law trend. This is done on the basis that the historical bottoms happen to coincide with this particular deviation from the trend.
2) A sinusoidal pulsating function that has a 4-year periodicity and is synchronized to the top of the first of the periodic BTC bubble.
3) An exponential decay fitted to the 3 observed bubbles to represent the empirical decay of the amplitude of these oscillations relative to the trend.

This full model is also represented as a "stretched spiral" in a polar graph.

Finally, given we want to represent the circular path of BTC in a linear graph we took the sine projection of the x and y polar coordinates of the simple model, the full model, and the daily price of BTC.

The usefulness of this script is that it represents in a single graph both the Power Law behavior of BTC but also its cyclic nature. Each quadrant of the spiral clock coincides with a precise market phase with 0 o'clock being the top, 3 o'clock being the bottom, 6 o'clock being the transition from the bear market to the bull market and 9 o'clock being the start of the full bull market.

It is recommended to use this oscillator together with the "Adaptive Power Law Fitting by G. Santostasi" TV indicator.

12 thg 5, 2024

Phát hành các Ghi chú

This script is based on G. Santostasi's Power Law Spiral Clock.
The Power Law Clock is a projection in polar coordinates of the Power Law Model of BTC price normalized to its natural periodicity of 4 years.

The Power Law model is derived by fitting the price of BTC in a log-log chart assuming that it has a long-term Polar Law Behavior. Using regression it is possible to extract the slope n (that is also the power of the power law) and the y-intercept. These parameters can be used to define a Power Law spiral of the form rho=A*theta^n, where theta is the time in days from the Genesis block normalized to the 4-year cycle.

The script represents 2 models the simple Power Law Spiral as defined above and a more full model with 3 components:
1) A power law trend that is adjusted to 2 standard deviations from the median Power Law trend. This is done on the basis that the historical bottoms happen to coincide with this particular deviation from the trend.
2) A sinusoidal pulsating function that has a 4-year periodicity and is synchronized to the top of the first of the periodic BTC bubble.
3) An exponential decay fitted to the 3 observed bubbles to represent the empirical decay of the amplitude of these oscillations relative to the trend.

This full model is also represented as a "stretched spiral" in a polar graph.

Finally, given we want to represent the circular path of BTC in a linear graph we took the sine projection of the x and y polar coordinates of the simple model, the full model, and the daily price of BTC.

The usefulness of this script is that it represents in a single graph both the Power Law behavior of BTC but also its cyclic nature. Each quadrant of the spiral clock coincides with a precise market phase with 0 o'clock being the top, 3 o'clock being the bottom, 6 o'clock being the transition from the bear market to the bull market and 9 o'clock being the start of the full bull market.

It is recommended to use this oscillator together with the "Adaptive Power Law Fitting by G. Santostasi" TV indicator.