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The Fractal Nature of Bitcoin: Evidence from Wavelet Power Spectra

Abstract

In this study, a continuous wavelet transform is performed on bitcoin’s historical returns. Despite the asset’s novelty and high volatility, evidence from the wavelet power spectra shows clear dominance of specific investment horizons during periods of high volatility. Thanks to wavelet analysis, it is also possible to observe the presence of fractal dynamics in the asset’s behavior. Wavelet analysis is a method to decompose a time series into several layers of time scales, making it possible to analyze how the local variance, or wavelet power, changes both in the frequency and time domain. Although relatively new to finance and economic, wavelet analysis represents a powerful tool that can be used to study how economic phenomena operate at simultaneous time horizons, as well as aggregated processes that are the result of several agents or variables with different term objectives.

Keywords

  • Fractal market hypothesis
  • Bitcoin
  • Wavelet power spectrum
  • Wolfram Mathematica
  • Economics and finance
  • Cryptocurrencies
  • Wavelet analysis

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  • DOI: 10.1007/978-3-319-32543-9_5
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Notes

  1. 1.

    This manuscript is based on the undergraduate thesis project of the first author (Delfin 2014) and supervised by the second author.

  2. 2.

    According to the Bitcoin wiki website (https://en.bitcoin.it/wiki/Introduction#Capitalization_.2F_Nomenclature), capitalization and nomenclature can be confusing since Bitcoin is both a currency and a protocol. Bitcoin, singular with an uppercase letter B, will be used to label the protocol, software, and community, and bitcoins, with a lowercase b, will be used to label units of the currency.

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Correspondence to Guillermo Romero-Meléndez .

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© 2016 Springer International Publishing Switzerland

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Delfin-Vidal, R., Romero-Meléndez, G. (2016). The Fractal Nature of Bitcoin: Evidence from Wavelet Power Spectra. In: Pinto, A., Accinelli Gamba, E., Yannacopoulos, A., Hervés-Beloso, C. (eds) Trends in Mathematical Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-32543-9_5

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