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

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  • Grobys, Klaus

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.

Suggested Citation

  • Grobys, Klaus, 2023. "A Fractal and Comparative View of the Memory of Bitcoin and S&P 500 Returns," Research in International Business and Finance, Elsevier, vol. 66(C).
    • Handle: RePEc:eee:riibaf:v:66:y:2023:i:c:s0275531923001472
    DOI: 10.1016/j.ribaf.2023.102021
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    Keywords

    Bitcoin; Fractals; Fractality; Hurst exponent; Memory; S&P 500; Statistical self-affine; Pareto distributions; Power laws; Second moment; Variance;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • O10 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - General

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