We consider a volatility model, named ARCH-NNH model, that is specifically an ARCH process with a nonlinear function of a persistent, integrated or nearly integrated, explanatory variable.We first establish the asymptotic theories showing that the time series properties of our model successfully...

We consider ARCH processes with persistent covariates and provide asymptotic theories that explain how such covariates affect various characteristics of volatility. Specifically, we propose and study a volatility model, named ARCH-NNH model, that is an ARCH(1) process with a nonlinear function...