Nonparametric Time Series Model Selection
Wolfgang Karl Härdle, Lijian Yang · 1996
Nonparametric procedures are an interesting alternative to classical time series analysis. The nonparametric technique follows the principle of `letting the data speak for themselves,' and provides guidance in choosing a parametric models. In this paper local polynomial estimators are given for vector conditional heteroskedastic autoregressive nonlinear (CHARN) model in which both the conditional mean and the conditional variance (volatility) matrix are unknown functions of the past. We examine the rates of convergence of these estimators and their asymptotic normality. These are applied to estimation of volatility matrices of foreign exchange rates. As the usual nonparametric models often have less than satisfactory performance when dealing with more than one lag, we also give the joint estimation of the additive mean and the multiplicative volatility, which fully exploits the additive/multiplicative structure. We then discuss the usefulness of this approach in selecting the correct l...