Volatility asymmetry in functional threshold GARCH model

Modeling volatility is one of the prime objectives of financial time‐series analysis. A significant feature encountered in the modeling of financial data is the asymmetric response to the volatility process of unanticipated shocks. With improvements in data acquisition, functional versions of the heteroskedastic models have emerged to deal with the high‐frequency observations. Although previous studies have developed some functional time‐series methods, it remains a necessity to analyze the variations in the asymmetry of the discrete model and the function model. In this study, we propose a functional threshold GARCH (fTGARCH) model and extend the news impact curve (NIC) and the cumulative impact response function (CIRF) within the functional heteroskedastic framework. We find that the fTGARCH model can describe the asymmetry of the observation data, which are revealed by the sample cross‐correlation functions. The slope of the NIC changes with time for functional GARCH class models, and the changes are asymmetrical for the fTGARCH model. Using the generalized CIRF, we can explore the persistent effects of volatility for the functional GARCH class models. By fitting the models to the S&P 500 stock market index, we conclude that the fTGARCH model has some flexibility and superiority in regard to volatility asymmetry.