Nonparametric Time-Series Estimation of Joint DGP, Conditional DGP, and Vector Autoregression

In this paper we develop nonparametric estimators of the joint time series data generating process (DGP) of (<italic>x</italic>, <italic>y</italic>) at different <italic>t</italic>-values, of conditional DGP, of the conditional mean of <italic>x</italic> given the past values of <italic>x</italic> and <italic>y</italic>, and, more generally, the conditional mean of (<italic>x</italic>, <italic>y</italic>) given their past values (vector autoregression). We establish, among other results, the central limit theorems for these estimators under far weaker mixing conditions than those used in Robinson [23], where only the <italic>x</italic> series is considered. Uniform consistency and rate results for the consistencies of various estimators are also obtained. The results of the paper are useful in light of the fact that often the functional form of the dynamic regression is not known and also the assumption of the Gaussian process is not true.