Predicting volatility of bitcoin returns with ARCH, GARCH and EGARCH models

Abstract

Abstract The ınvestment decisions of institutional and individual investors in financial markets are largely influenced by market uncertainty and volatility of the investment instruments. Thus, the prediction of the uncertainty and volatilities of the prices and returns of the investment instruments becomes imperative for successful investment. In this study we seek to identify the best fit model that can predict the volatility of return of Bitcoin, which is in high demand as an investment tool in recent times. Using the opening data of weekly Bitcoin prices for the period of 11.24.2013–03.22.2020, their logarithmic returns were calculated. The stationarity properties of the Bitcoin return series was tested by applying the ADF unit root test and the series were found to be stationary. After reaching the average equation model as ARMA (2.2), it was tested whether there was an ARCH effect in the ARMA (2,2) model. As a result of the applied ARCH-LM test, it is reached that the residuals of the average equation model selected have ARCH effect. Volatility of Bitcoin return series after detection of ARCH effect has been tried to predict with conditional variance models such as ARCH (1), ARCH (2), ARCH (3), GARCH (1,1), GARCH (1,2), GARCH (1,3), GARCH (2,1), GARCH (2,2), EGARCH (1,1) and EGARCH (1,2). While the obtained findings indicate that the best model is in the direction of GARCH (1,1) according to Akaike info criterion, it was found that GARCH (1,1) model does not have ARCH effect as a result of the applied ARCH-LM test. Thus, our empirical findings highlight an ample guide on appropriate modeling of price information in the Bitcoin market.

Keywords

• Bitcoin volume
• Volatility returns
• ARMA
• ARCH
• GARCH