GARCH Process with Persistent Covariates

GARCH Process with Persistent Covariates

While most ARCH type models have been univariate, many previous works considered the GARCH(1,1) model with persistent covariates to provide economic explanations for volatility. Generalizing the model, we consider the GARCH-NNH model, which is a GARCH(1,1) process with a nonlinear function of a persistent, integrated or nearly integrated, variable. Based on the work of the nonlinear regression with integrated time series by Park and Phillips (2001), we derive various asymptotic results related to the model. First, we establish the asymptotic distribution theory of the QMLE in the GARCH-NNH model. It is shown that the QMLE is consistent and its asymptotic distribution is mixed normal. Second, we provide asymptotic theories showing how the GARCH-NNH model explains the stylized facts of volatility in …nancial time series. It is shown that the model successfully explains the long memory property in volatility, leptokurtosis and the IGARCH behavior.