Different GARCH model analysis on returns and volatility in Bitcoin

Abstract

<abstract> <p>The aim of this study was to examine the returns and volatility of Bitcoin. The study uses the daily closing price of Bitcoin from October 1, 2013 to July 31, 2020 as the sample data, which include 2496 observations. About the methodology, the paper describes the utilisation of GARCH models to analyse Bitcoin's returns and volatility. First, the data were tested by using the augmented Dickey-Fuller test to verify the stability and diagram tests sequence. After that, the lag order and determination results of the mean value equation show that the Lag 4 period is the best. Additionally, the paper describes an autocorrelation test of the residual series, which revealed that there is no significant autocorrelation in the residual term for the Bitcoin returns, but that the residual squared has significant autocorrelation. In addition, a linear graph of squared residuals was formulated and the ARCH-LM test was used to find the data that are suitable for modelling with GARCH models since the data have a strong ARCH effect. As result, a GARCH (1, 1) model was used; the findings indicated that the returns and volatility of Bitcoin have clustering characteristics, and that the returns and volatility of Bitcoin constitute a persistent process although the effects gradually reduce over time. Because of the limitations of the GARCH (1, 1) model and researching asymmetry of the returns and volatility of Bitcoin, TARCH and EGARCH models were adopted; the findings indicated that the returns and volatility of Bitcoin are without a "leverage effect". To further explain this special phenomenon, safe-property is quoted in this research. In the end, this paper demonstrates that Bitcoin, as a safe-haven property, can hedge financial risks in times of economic depression. Besides, Bitcoin has a revised asymmetric effect between positive and negative shocks that makes it a viable asset to add to the portfolios of investors.</p> </abstract>