Long memory and efficiency of Bitcoin under heavy tails

Abstract

The long memory is usually defined via auto-covariances which further connect with Hurst exponent. The heavy tails in Bitcoin returns can cause infinite auto-covariances which make the analysis of long memory and market efficiency in Bitcoin based on estimation of Hurst exponent inappropriate. Few literatures focus on this problem. We provide two approaches based on shuffling method and rank-ordered technique to this problem, and further combine them to analyse the time-varying efficiency and long memory in Bitcoin using sliding window. Results show that the inefficiency and long memory exist in Bitcoin before 2014 and after mid-2017. Especially, the latest data reveal a recent new change that the Bitcoin market has become inefficient and exhibited long memory behaviour since mid-2017, but is turning back to efficiency recently. This change may be due to the frequent key events of Bitcoin in 2017 and 2018, which can break the weak efficiency of Bitcoin. The heavy negative tails with α<2 before September 2016 validate the necessity of our analysis under heavy tails. Besides, the change trend and exact sub-periods of efficiency and long memory are first obtained via empirical mode decomposition of Hurst exponent estimates.