Nonparametric Estimators for Time Series

Abstract. Kernel multivariate probability density and regression estimators are applied to a univariate strictly stationary time series X r We consider estimators of the joint probability density of X t at different t ‐values, of conditional probability densities, and of the conditional expectation of functionals of X v given past behaviour. The methods seem of particular relevance in light of recent interest in non‐Gaussian time series models. Under a strong mixing condition multivariate central limit theorems for estimators at distinct points are established, the asymptotic distributions being of the same nature as those which would derive from independent multivariate observations.