A Fractal and Comparative View of the Memory of Bitcoin and S&P 500 Returns

Klaus Grobys

Research in International Business and Finance, 2023, vol. 66, issue C

Abstract: The majority of previous studies used autocorrelation-based methodologies to explore the dependency structure for Bitcoin, but this paper follows Benoit Mandelbrot in taking a fractal point of view. This perspective showed that Bitcoin and S&P 500 returns exhibit fractal-like behavior. Additional evidence suggested that the infinite variance hypothesis cannot be rejected for either asset supporting Mandelbrot’s (1963) early study on cotton price changes. This result held across non-overlapping subsamples. Following Mandelbrot (2008), Hurst exponents were estimated using rescaled/range analysis. The key findings are that (a) Bitcoin returns exhibit a higher level of persistence than S&P 500 returns across various subsamples, (b) the level of persistence in Bitcoin returns did not change over time, (c) the S&P 500 moved from efficiency in the first subsample to inefficiency in the ex-post June 17, 2018, period, (d) even if it was assumed that the variance of S&P 500 returns was finite, the kurtosis remained statistically undefined. The study concluded that the correlation-based methods used to explore the S&P 500 universe result in misleading answers.

Keywords: Bitcoin; Fractals; Fractality; Hurst exponent; Memory; S&P 500; Statistical self-affine; Pareto distributions; Power laws; Second moment; Variance (search for similar items in EconPapers)
JEL-codes: C22 G12 G13 G14 O10 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:riibaf:v:66:y:2023:i:c:s0275531923001472

DOI: 10.1016/j.ribaf.2023.102021

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