Price Appreciation and Roughness Duality in Bitcoin: A Multifractal Analysis

Since its launch in 2009, bitcoin has thrived, attracting the attention of investors, regulators, academia, and the public in general. Its price dynamics, characterized by extreme volatility, severe jumps, and impressive long-term appreciation, suggest that bitcoin is a new digital asset. This study presents a comprehensive overview of the fractality of bitcoin in a high-frequency framework, namely by applying Multifractal Detrended Fluctuation Analysis (MF-DFA) and a Multifractal Regime Detecting Method (MRDM) to Bitstamp 1 min bitcoin returns from January 2013 to July 2020. The results suggest that bitcoin is multifractal, with smaller and larger fluctuations being persistent and anti-persistent, respectively. Multifractality comes from significant long-range correlations, which cast some doubts on the informational efficiency at this frequency, but mainly comes from fat-tails, which highlights the significant risks undertaken by investors in this market. Our most important result is that the degree and richness of multifractality is time-varying and increased after 2017, when volumes and prices experienced an explosive behaviour. This complexity puts into perspective the duality of bitcoin: while it is characterized by long-run attractiveness and increasing valuation, it also has a high short-run instability. Hence, this study provides some empirical evidence supporting the relationship between these two observable features.