Is Bitcoin Really Following a Power Law Trend

If you look at Bitcoin charts long enough, you start seeing all kinds of neat patterns and trend lines. One popular idea claims Bitcoin follows a power law, meaning its price growth slows down in a predictable way as it ages. I came across a new study that puts this famous power law math to a strict reality check. It turns out that noisy price movements can easily trick people into seeing trends that might not be real.

The researchers wanted to see if fifteen years of weekly prices could truly prove a power-law trend. They built a strict test using a noise model with a four-year cycle and declining volatility. To keep things honest, they publicly hashed their test method before applying it a single time. Constant price growth was rejected at nominal 5% while a log-age coefficient of 5.7 was not rejected. But that rejection falls apart if price noise is more persistent than a random walk. A Gompertz curve with a ceiling fits about as well, so nobody can prove yet whether prices actually pull back to a trend line. Registered forecasts for 2027 to 2030 will eventually show how the math holds up.

The study behind all this is Deceleration without identification: testing a power-law trend in Bitcoin prices under persistent noise by Carlos Baquero and Raquel Menezes. It lives at arxiv.org/abs/2611.13962 if you feel like reading more. I only tried to make the abstract easier to digest.

This is not financial advice. The information provided is for educational and informational purposes only.

The cover image was generated by AI.