On the threshold hyperbolic GARCH models

In the financial market, the volatility of financial assets plays a key role in the problem of measuring market risk in many investment decisions. Insights into economic forces that may contribute to or amplify volatility are thus important. The financial market is characterized by regime switching between phases of low volatility and phases of high volatility. Nonlinearity and long memory are two salient features of volatility. To jointly capture the features of long memory and nonlinearity, a new threshold time series model with hyperbolic generalized autoregressive conditional heteroscedasticity is considered in this article. A goodness of fit test is derived to check the adequacy of the fitted model. Simulation and empirical results provide further support to the proposed model.