Purpose: The purpose of our study was to examine the property of long memory in the mean and volatility of daily returns on two major cryptocurrencies – Bitcoin and Ethereum – over the period ranging from January 1, 2017, to December 1, 2022. The growing body of research on this relatively new asset class, cryptocurrencies, motivated us to conduct this study.

Methodology: We used autoregressive fractionally integrated moving average (ARFIMA) and fractionally integrated generalized autoregressive conditional heteroscedasticity (FIGARCH) models to study long-memory in both mean returns and volatility of Bitcoin and Ethereum. The study also employed Bai–Perron and Quandt–Andrews tests to identify structural breaks in both cryptocurrencies, allowing for a more detailed examination of the property of long-memory in sub-samples.

Findings: Our results confirmed the absence of long memory in mean returns on Bitcoin for the whole sample period as well as both sub-sample periods, implying that its market is efficient. Mean returns on Ethereum exhibited long memory over the complete sample period; however, the sub-sample analysis revealed a shift toward market efficiency, as long memory was not present in the second sub-sample. The results from FIGARCH analysis confirmed the prevalence of long-memory in the volatility of returns on both Bitcoin and Ethereum.

Implications: The mean returns for both cryptocurrencies did not show persistence in the second sub-sample period, which was characterized by heightened economic uncertainty. This implies that external events did not have predictive power over cryptocurrencies. However, the presence of long memory in volatility implied that past volatility levels affected present volatility levels in both cryptocurrencies. Therefore, investors and policymakers could use volatility predictions to assess riskiness in their portfolios and the cryptocurrency market to formulate regulations, respectively.

Originality: The paper contributed to the rather sparse body of literature pertaining to properties of financial time series with respect to cryptocurrency. An important contribution of this paper is to provide a comprehensive study, accommodating a structural break, over a period that includes periods of low and high economic uncertainty.

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