A K-means clustering model for analyzing the Bitcoin extreme value returns

Abstract

Bitcoin prices are highly volatile and have extreme upper tails of the return distributions. One important component of Bitcoin price jumps is that it does not follow a normal distribution. This present study aims to reduce the extreme value data available on Bitcoin into simple clusters based on extreme value returns. The study first measures the excessive volatility and then estimates the extreme value returns of Bitcoin between November 2013 and August 2022 to achieve this objective. For robustness checks, extreme value returns are estimated using both the Rogers and Satchell (RS) and the Variance Ratio (VRatio) estimators that embed jumps in the model. Further, K-means clustering is used to form clusters based on the estimated Bitcoin’s extreme value returns as the probable good days (extreme days), medium days, and bad days. The study observes that K-means clustering can explain 65 percent point return variability. The study findings will be highly useful for crypto investors, policymakers, and future studies in data mining.