Bitcoin Return Tails and Volatility Scaling

Summary

This study examines whether Bitcoin returns follow the heavy-tail patterns reported in earlier work and how volatility behaves over time. Earlier estimates placed the cumulative-return tail index near two, while many other assets show an index near three. Using more recent Bitcoin data, the study finds an index near three, suggesting the tail behavior can change across sample periods.

It also analyzes autocorrelation in absolute returns, finding a power-law pattern with two scaling exponents. After standardizing returns by realized volatility, the series is consistent with normally distributed returns whose volatility varies over time. The results describe statistical properties rather than a trading strategy, and the excerpt gives no details on the sample dates, estimation procedures, uncertainty, or robustness checks. The findings therefore support a time-varying volatility interpretation but do not establish that the same distributional behavior will persist in future data.

Key ideas

• Recent Bitcoin return data show a tail index near three, differing from earlier estimates near two.
• The cumulative-return tail behavior may vary across market periods.
• Absolute-return autocorrelation follows a power law with two scaling exponents.
• Returns standardized by realized volatility are consistent with normal variables under time-varying volatility.

Tags

# Recent scaling properties of Bitcoin price returns


# Recent scaling properties of Bitcoin price returns









While relevant stylized facts are observed for Bitcoin markets, we find a distinct property for the scaling behavior of the cumulative return distribution. For various assets, the tail index $μ$ of the cumulative return distribution exhibits $μ\approx 3$, which is referred to as "the inverse cubic law." On the other hand, that of the Bitcoin return is claimed to be $μ\approx 2$, which is known as "the inverse square law." We investigate the scaling properties using recent Bitcoin data and find that the tail index changes to $μ\approx 3$, which is consistent with the inverse cubic law. This suggests that some properties of the Bitcoin market could vary over time. We also investigate the autocorrelation of absolute returns and find that it is described by a power-law with two scaling exponents. By analyzing the absolute returns standardized by the realized volatility, we verify that the Bitcoin return time series is consistent with normal random variables with time-varying volatility.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.