Nonparametric regression for locally stationary time series

TL;DR

This paper develops a kernel-based nonparametric approach to estimate smoothly changing regression functions in locally stationary time series, extending models with time-varying coefficients and addressing high-dimensional additive structures.

Contribution

It introduces a novel kernel-based estimation method for locally stationary regressions and provides asymptotic theory applicable to nonlinear autoregressive processes.

Findings

Estimation method is consistent under broad conditions.

Main conditions hold for nonlinear autoregressive models.

Structured additive models avoid curse of dimensionality.

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.