NONPARAMETRIC REGRESSION FOR LOCALLY STATIONARY TIME SERIES

作者：Vogt Michael^*

来源：Annals of Statistics, 2012, 40(5): 2601-2633.

DOI：10.1214/12-AOS1043

• Local stationarity
• nonparametric regression
• smooth backfitting

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.

• 出版日期2012-10