Different GARCH models analysis of returns and volatility in Bitcoin

To research returns and volatility of Bitcoin (BTC), this paper uses daily closing price of Bitcoin from October 1st, 2013 to July 31th, 2020 to be sample data, and there are 2496 observations in the data. In methodology, the paper utilizes GARCH models to analyze Bitcoin's returns and volatility. Firstly, the data is tested by ADF test to verify stability and diagram tests sequence. After that, lag order and determination of mean value equation shows lag 4 period is the best. Besides, the paper does autocorrelation test of residual series and find that there is no significant autocorrelation in the residual term of the Bitcoin returns, but the residual squared has significant autocorrelation. In addition, the paper makes a linear graph of squared residuals and use ARCH-LM test to find the data is suitable to modeling by GARCH models, because the data has strong ARCH effect. In results, this paper use GARCH (1, 1) model to find that returns and volatility of Bitcoin have clustering characteristics and returns and volatility of Bitcoin is a persistent process, but its effect gradually reduces by the time. Because of limitation of GARCH (1, 1) model and researching asymmetry of returns and volatility of Bitcoin, this paper uses TARCH and EGARCH models to find that returns and volatility of Bitcoin is without "Leverage Effect". In order to further explaining this special phenomenon, safe-property is quoted in this research. In the end, this paper finds that Bitcoin as a safe-haven property can hedge financial risks in economic depression time, and it has a revised asymmetric effect between positive and negative shocks, so it is a conducive asset to add into portfolios of investors.