Modeling Conditional Variance Functions in Nonparametric Transfer Function Models

Estimating conditional variance functions is of great importance in practice. We propose an efficient method to estimate conditional variance functions in nonparametric transfer function models. The main idea is using polynomial splines to approximate the transfer function and the conditional variance function. We show that the conditional variance functions can be estimated as if the transfer function is known, and the ARMA parameters can be estimated with the usual parametric rate of convergence. The asymptotic properties of the estimators are investigated and the finite-sample properties of the estimators are illustrated through simulations and one real data example.