Volatility Modelling of Cryptocurrencies According to Different Investment Horizons: The Case of Bitcoin

Abstract

In this study, the fractal structure, efficiency, and long memory features of Bitcoin are investigated according to different investment horizons. The study utilized daily returns from 01.01.2017 to 22.11.2023, applying the maximum overlap discrete wavelet transform, Rescaled Range (R/S) analysis, and volatility models. The analysis results revealed a deviation of Bitcoin returns from the average and a negative correlation, indicating a lack of permanent behaviour in the series. The analysis demonstrates the rejection of the efficient market hypothesis and reveals a chaotic structure in the Bitcoin market. Furthermore, we observed a hyperbolic rate of decrease in returns at long-term investment horizons due to information shocks. This indicates that past returns can predict future returns. This suggests that instead of the efficient market hypothesis, the fractal market hypothesis is valid due to the existence of recurring trends. Finally, we determined the most appropriate volatility models for Bitcoin. The analysis shows that information shocks in Bitcoin returns at medium- and long-term investment horizons decrease over time, and past returns can predict future returns. However, volatility and information shocks are transitory at short- and medium-term investment horizons but can vary. All analysis methods yield consistent and compatible results, suggesting their potential extension to other cryptocurrency markets beyond the Bitcoin market.