Predicting the volatility of Bitcoin returns based on kernel regression

Abstract

Nonparametric regression has become a popular method because it offers great flexibility in data modeling without requiring a precise description of the functional forms of estimated models. With the onset of the coronavirus pandemic, Bitcoin, a historically volatile cryptocurrency, has emerged as one of the most contentious issues due to the potential for banknotes to facilitate the transmission of viruses. This paper aimed to predict the volatility of Bitcoin returns using squared and original returns as proxies for volatility and to perform the quantile estimation for different prediction horizons for the period September 17th, 2014-March 13th, 2020 by implementing a kernel regression approach based on the exponentially weighted moving average (EWMA), presenting the comparison results along with various volatility predictors, and employing cross-validation. When handling generalized autoregressive conditional heteroscedasticity (GARCH) and EWMA predictors jointly for the prediction horizon of one beginning in mid-2017, aggregated EWMA and Heston-Nandi (HN) GARCH(1,1) predictors outperformed the standard GARCH(1,1) predictor, and among EWMA predictors, aggregated predictors are superior when skewness parameter is less than 0.5. In addition, for a prediction horizon of 1 day, GARCH(1,1) volatility as the kernel predictor has outperformed the standard GARCH(1,1) predictor over all time periods. However, as the prediction horizon is expanded above 10, the EWMA volatility performs better than GARCH volatility.