Bitcoin Power Law: Complete with Oscillator + Future Projection

Firstly, we would like to give credit to @apsk32 and @x_X_77_X_x as part of the code originates from their work. Additionally, @apsk32 is widely credited with applying the Power Law concept to Bitcoin and popularizing this model within the crypto community. Additionally, the visual layout is fully inspired by @apsk32's designs, and we think it looks amazing. So much so that we had to turn it into a TradingView script. Thank you!

Understanding the Bitcoin Power Law Model
Also called the Long-Term Bitcoin Power Law Model. The Bitcoin Power Law model tries to capture and predict Bitcoin's price growth over time. It assumes that Bitcoin's price follows an exponential growth pattern, where the price increases over time according to a mathematical relationship.

By fitting a power law to historical data, the model creates a trend line that represents this growth. It then generates additional parallel lines (support and resistance lines) to show potential price boundaries, helping to visualize where Bitcoin’s price could move within certain ranges.

In simple terms, the model helps us understand Bitcoin's general growth trajectory and provides a framework to visualize how its price could behave over the long term.

The Bitcoin Power Law has the following function:
Power Law = 10^(a + b * log10(d))

Consisting of the following parameters:

• a: Power Law Intercept (default: -17.668).
  
• b: Power Law Slope (default: 5.926).
  
• d: Number of days since a reference point(calculated by counting bars from the reference point with an offset).

Explanation of the a and b parameters:
Roughly explained, the optimal values for the a and b parameters are determined through a process of linear regression on a log-log scale (after applying a logarithmic transformation to both the x and y axes). On this log-log scale, the power law relationship becomes linear, making it possible to apply linear regression. The best fit for the regression is then evaluated using metrics like the R-squared value, residual error analysis, and visual inspection. This process can be quite complex and is beyond the scope of this post.

Applying vertical shifts to generate the other lines:
Once the initial power-law is created, additional lines are generated by applying a vertical shift. This shift is achieved by adding a specific number of days (or years in case of this script) to the d-parameter. This creates new lines perfectly parallel to the initial power law with an added vertical shift, maintaining the same slope and intercept.

In the case of this script, shifts are made by adding +365 days, +2 * 365 days, +3 * 365 days, +4 * 365 days, and +5 * 365 days, effectively introducing one to five years of shifts. This results in a total of six Power Law lines, as outlined below (From lowest to highest):

• Base Power Law Line (no shift)
  
• 1-year shifted line
  
• 2-year shifted line
  
• 3-year shifted line
  
• 4-year shifted line
  
• 5-year shifted line

The six power law lines:


Bitcoin Power Law Oscillator
This publication also includes the oscillator version of the Bitcoin Power Law. This version applies a logarithmic transformation to the price, Base Power Law Line, and 5-year shifted line using the formula log10(x).

The log-transformed price is then normalized using min-max normalization relative to the log-transformed Base Power Law Line and 5-year shifted line with the formula:

normalized price = log(close) - log(Base Power Law Line) / log(5-year shifted line) - log(Base Power Law Line)

Finally, the normalized price was multiplied by 5 to map its value between 0 and 5, aligning with the shifted lines. The Oscillator version can be found here.

Interpretation of the Bitcoin Power Law Model:
The shifted Power Law lines provide a framework for predicting Bitcoin's future price movements based on historical trends. These lines are created by applying a vertical shift to the initial Power Law line, with each shifted line representing a future time frame (e.g., 1 year, 2 years, 3 years, etc.).

By analyzing these shifted lines, users can make predictions about minimum price levels at specific future dates. For example, the 5-year shifted line will act as the main support level for Bitcoin’s price in 5 years, meaning that Bitcoin’s price should not fall below this line, ensuring that Bitcoin will be valued at least at this level by that time. Similarly, the 2-year shifted line will serve as the support line for Bitcoin's price in 2 years, establishing that the price should not drop below this line within that time frame.

On the other hand, the 5-year shifted line also functions as an absolute resistance, meaning Bitcoin's price will not exceed this line prior to the 5-year mark. This provides a prediction that Bitcoin cannot reach certain price levels before a specific date. For example, the price of Bitcoin is unlikely to reach $100,000 before 2021, and it will not exceed this price before the 5-year shifted line becomes relevant. After 2028, however, the price is predicted to never fall below $100,000, thanks to the support established by the shifted lines.

In essence, the shifted Power Law lines offer a way to predict both the minimum price levels that Bitcoin will hit by certain dates and the earliest dates by which certain price points will be reached. These lines help frame Bitcoin's potential future price range, offering insight into long-term price behavior and providing a guide for investors and analysts. Lets examine some examples:

Example 1:

In Example 1 it can be seen that point A on the 5-year shifted line acts as major resistance. Also it can be seen that 5 years later this price level now corresponds to the Base Power Law Line and acts as a major support (Note: Vertical yearly grid lines have been added for this purpose👍).

Example 2:

In Example 2, the price level at point C on the 3-year shifted line becomes a major support three years later at point C, now aligning with the Base Power Law Line.

Finally, let's explore some future price predictions, as this script provides projections on the weekly timeframe :

Example 3:

In Example 3, the Bitcoin Power Law indicates that Bitcoin's price cannot surpass approximately 808K before 2030 as can be seen at point E, while also ensuring it will be at least 224K by then (point F).


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