Abstract
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.
Highlights
The history of bitcoin begins on 31 October 2008, when the pseudonym SatoshiNakamoto published a white paper on an electronic peer-to-peer payment system without physical representation based on cryptography [1]
This study examines multifractality in bitcoin high-frequency returns using Multifractal Detrended Fluctuation Analysis (MF-DFA) [11]
The economics and finance literature on cryptocurrencies and most notably on bitcoin has been piling up at an impressive rate, due to its impressive price appreciation, trading volume, and market capitalization. Most of this literature gathers evidence on stylized facts of bitcoin price dynamics, which appear to be different from currency exchange rates or other financial assets traded in regulated markets
Summary
Nakamoto published a white paper on an electronic peer-to-peer payment system without physical representation based on cryptography [1]. The causal relation runs from investor heterogeneity to market liquidity and from market liquidity to market stability This efficiency hypothesis was named “fractal” because it implies a self-similar structure—a characteristic of fractals—i.e., investors should share the same levels of risk, because long-term investors will counterbalance short-term investors to keep the market stable. This trading time reflects the fact that market activity and the resulting price dynamics change through different periods and mimics the apparent intermittency in observed paths Models based on this multifractal representation are parsimonious and empirically well-adjusted since the time deformation introduced acts in many scales, not just in one as happens with GARCH-type models.
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