Bitcoin Return Long Memory and Multiscale Self-Similarity

Summary

The paper examines statistical properties of Bitcoin returns, compares their dynamics with those of conventional currencies, and considers behavior across time scales. Its empirical sample consists of transaction data from a single Bitcoin platform over the period studied. To assess long-range dependence, it applies detrended fluctuation analysis and calculates Hurst exponents in sliding windows, allowing the estimated persistence to vary over time.

The reported estimates change substantially during Bitcoin’s early years and tend to become more stable later in the sample. The multiscale results show similar Hurst-exponent behavior, which the authors interpret as evidence of self-similarity. These findings describe historical statistical patterns; they do not establish a profitable trading signal or show that the observed dependence will persist. The single-platform data and finite historical period also limit how broadly the results can be generalized to Bitcoin markets or future conditions.

Key ideas

• The study compares Bitcoin return dynamics with those of standard currencies.
• Detrended fluctuation analysis is used to estimate long-range dependence.
• Sliding windows track how Hurst exponents change through the sample.
• The estimates shift during Bitcoin’s early years and later tend to stabilize.
• Multiscale estimates show similar behavior, interpreted as self-similarity.

Tags

# Some stylized facts of the Bitcoin market


# Some stylized facts of the Bitcoin market









In recent years a new type of tradable assets appeared, generically known as cryptocurrencies. Among them, the most widespread is Bitcoin. Given its novelty, this paper investigates some statistical properties of the Bitcoin market. This study compares Bitcoin and standard currencies dynamics and focuses on the analysis of returns at different time scales. We test the presence of long memory in return time series from 2011 to 2017, using transaction data from one Bitcoin platform. We compute the Hurst exponent by means of the Detrended Fluctuation Analysis method, using a sliding window in order to measure long range dependence. We detect that Hurst exponents changes significantly during the first years of existence of Bitcoin, tending to stabilize in recent times. Additionally, multiscale analysis shows a similar behavior of the Hurst exponent, implying a self-similar process.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.