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arXiv · 1302.4198

Nonparametric regression for locally stationary time series

Michael Vogt
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Abstract

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We introduce a kernel-based method to estimate the time-varying regression function and provide asymptotic theory for our estimates. Moreover, we show that the main conditions of the theory are satisfied for a large class of nonlinear autoregressive processes with a time-varying regression function. Finally, we examine structured models where the regression function splits up into time-varying additive components. As will be seen, estimation in these models does not suffer from the curse of dimensionality.

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Michael Vogt. 2013-02-18. Nonparametric regression for locally stationary time series. https://doi.org/10.1214/12-aos1043

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