Bitcoin Polynomial Regression Model

This is the main version of the script. Click here for the Oscillator part of the script.

💡Why this model was created:
One of the key issues with most existing models, including our own Bitcoin Log Growth Curve Model, is that they often fail to realistically account for diminishing returns. As a result, they may present overly optimistic bull cycle targets (hence, we introduced alternative settings in our previous Bitcoin Log Growth Curve Model).

This new model however, has been built from the ground up with a primary focus on incorporating the principle of diminishing returns. It directly responds to this concept, which has been briefly explored here.


📉The theory of diminishing returns:
This theory suggests that as each four-year market cycle unfolds, volatility gradually decreases, leading to more tempered price movements. It also implies that the price increase from one cycle peak to the next will decrease over time as the asset matures. The same pattern applies to cycle lows and the relationship between tops and bottoms. In essence, these price movements are interconnected and should generally follow a consistent pattern. We believe this model provides a more realistic outlook on bull and bear market cycles.

To better understand this theory, the relationships between cycle tops and bottoms are outlined below:


🔧Creation of the model:
For those interested in how this model was created, the process is explained here. Otherwise, feel free to skip this section.

This model is based on two separate cubic polynomial regression lines. One for the top price trend and another for the bottom. Both follow the general cubic polynomial function:
ax^3 +bx^2 + cx + d.

In this equation, x represents the weekly bar index minus an offset, while a, b, c, and d are determined through polynomial regression analysis. The input (x, y) values used for the polynomial regression analysis are as follows:

Top regression line (x, y) values:

• 113, 18.6
  
• 240, 1004
  
• 451, 19128
  
• 655, 65502
  

Bottom regression line (x, y) values:

• 103, 2.5
  
• 267, 211
  
• 471, 3193
  
• 676, 16255
  

The values above correspond to historical Bitcoin cycle tops and bottoms, where x is the weekly bar index and y is the weekly closing price of Bitcoin. The best fit is determined using metrics such as R-squared values, residual error analysis, and visual inspection. While the exact details of this evaluation are beyond the scope of this post, the following optimal parameters were found:

Top regression line parameter values:

• a: 0.000202798
  
• b: 0.0872922
  
• c: -30.88805
  
• d: 1827.14113
  

Bottom regression line parameter values:

• a: 0.000138314
  
• b: -0.0768236
  
• c: 13.90555
  
• d: -765.8892
  

📊Polynomial Regression Oscillator:
This publication also includes the oscillator version of the this model which is displayed at the bottom of the screen. The oscillator applies a logarithmic transformation to the price and the regression lines using the formula log10(x).

The log-transformed price is then normalized using min-max normalization relative to the log-transformed top and bottom regression line with the formula:

normalized price = log(close) - log(bottom regression line) / log(top regression line) - log(bottom regression line)

This transformation results in a price value between 0 and 1 between both the regression lines. The Oscillator version can be found here.


🔍Interpretation of the Model:
In general, the red area represents a caution zone, as historically, the price has often been near its cycle market top within this range. On the other hand, the green area is considered an area of opportunity, as historically, it has corresponded to the market bottom.

The top regression line serves as a signal for the absolute market cycle peak, while the bottom regression line indicates the absolute market cycle bottom.

Additionally, this model provides a predicted range for Bitcoin's future price movements, which can be used to make extrapolated predictions. We will explore this further below.


🔮Future Predictions:
Finally, let's discuss what this model actually predicts for the potential upcoming market cycle top and the corresponding market cycle bottom. In our previous post here, a cycle interval analysis was performed to predict a likely time window for the next cycle top and bottom:

In the image, it is predicted that the next top-to-top cycle interval will be 208 weeks, which translates to November 3rd, 2025. It is also predicted that the bottom-to-top cycle interval will be 152 weeks, which corresponds to October 13th, 2025. On the macro level, these two dates align quite well. For our prediction, we take the average of these two dates: October 24th 2025. This will be our target date for the bull cycle top.

Now, let's do the same for the upcoming cycle bottom. The bottom-to-bottom cycle interval is predicted to be 205 weeks, which translates to October 19th, 2026, and the top-to-bottom cycle interval is predicted to be 259 weeks, which corresponds to October 26th, 2026. We then take the average of these two dates, predicting a bear cycle bottom date target of October 19th, 2026.

Now that we have our predicted top and bottom cycle date targets, we can simply reference these two dates to our model, giving us the Bitcoin top price prediction in the range of 152,000 in Q4 2025 and a subsequent bottom price prediction in the range of 46,500 in Q4 2026.

For those interested in understanding what this specifically means for the predicted diminishing return top and bottom cycle values, the image below displays these predicted values. The new values are highlighted in yellow:

And of course, keep in mind that these targets are just rough estimates. While we've done our best to estimate these targets through a data-driven approach, markets will always remain unpredictable in nature. What are your targets? Feel free to share them in the comment section below.