The Annals of Statistics
- Ann. Statist.
- Volume 40, Number 5 (2012), 2601-2633.
Nonparametric regression for locally stationary time series
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.
Ann. Statist., Volume 40, Number 5 (2012), 2601-2633.
First available in Project Euclid: 4 February 2013
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Vogt, Michael. Nonparametric regression for locally stationary time series. Ann. Statist. 40 (2012), no. 5, 2601--2633. doi:10.1214/12-AOS1043. https://projecteuclid.org/euclid.aos/1359987532
- Supplementary material: Additional technical details. The proofs and technical details that are omitted in the Appendices are provided in the supplement that accompanies the paper.