Semi-Nonparametric Generalized Autoregressive Conditional Heteroscedasticity Model with Application to Bitcoin Volatility Estimation

This study raises the problem of modeling conditional volatility under the random shocks’ normality assumption violation. To obtain more accurate estimates of GARCH process parameters and conditional volatilities, we propose two semi-nonparametric GARCH models. The implementation of the proposed methods is based on an adaptation of the [Gallant, Nychka, 1987] semi-nonparametric method to the family of GARCH models. The approach provides a flexible estimation procedure by approximating the unknown density of random shocks both using po­lynomials (PGN-GARCH) and splines (SPL-GARCH). To study the properties of the obtained estimators and compare them with alternatives, we conducted an ana­lysis of simulated data considering forms of distributions other than normal. As a result, statistical evidence was found in favor of the significant advantage of the proposed methods over the classical GARCH model and some other counterparts introduced earlier in the literature. Further, the proposed PGN-GARCH and SPL-GARCH models were applied to study Bitcoin conditional volatility dynamics. Du­ring the analysis, we found statistical evidence that Bitcoin distribution of shocks in returns differs from normal. Probably due to this reason the proposed SPL-GARCH model was able to demonstrate an advantage over alternative GARCH models according to the information criteria.