On the consistency and finite-sample properties of nonparametric kernel time series regression, autoregression and density estimators

Robinson, P. (1986). On the consistency and finite-sample properties of nonparametric kernel time series regression, autoregression and density estimators. Annals of the Institute of Statistical Mathematics, 38(1), 539-549. https://doi.org/10.1007/BF02482541
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Kernel estimators of conditional expectations and joint probability densities are studied in the context of a vector-valued stationary time series. Weak consistency is established under minimal moment conditions and under a hierarchy of weak dependence and bandwidth conditions. Prompted by these conditions, some finite-sample theory explores the effect of serial dependence on variability of estimators, and its implications for choice of bandwidth.

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