55 — The inefficiency of Bitcoin revisited: a dynamic approach

More than $17MM worth of Bitcoin exchange hands every day, and, despite some precipitous crashes, the value of BTC has skyrocketed since its inception. This paper begins by reviewing such papers as Donier & Bouchaud (2015) or Urquhart (2016) which tested measures of analysis for the Bitcoin market including autopredictiveness and correlations between local nonlinearities and long-term BTC returns.

This paper proposes Detrended Fluctuation Analysis (rather than R/S), to characterize the patterns and range of deviations of a time-series from its mean. For example, a straight line has both a DFA and RS measure equal to zero; but for a variant, Brownian time-series, this paper proposes that DFA holds valuable information; because the DFA statistic can be “windowed”, it can capture and amplify signal that persists only for a short period of the timeseries data. For example, if BTC traded differently for a few months, that signal could be captured by a windowed DFA.

Side-note: Mandelbrot worked on economic time-series analysis, which is unsurprising because Brownian motion is fractal-like in nature. (Before Relativity, Einstein focused on Brownian motion in diffusivity. This is a well-trodden field.)

The paper finds that DFA reveals two very different sub-series in the BTC analysis that are largely lost by R/S: Pre-2014, (with Hurst exponents greater than 0.5) daily returns are consistent; post-2014, Hurst exponents drop to a far more consistent ~0.5, indicating a noisier market. The reason for this sudden market destabilization is not clear, but this does show that “volatility clustering is a key feature of the Bitcoin market.”