The Annals of Statistics

Nonparametric regression for locally stationary time series

Michael Vogt

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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.

Article information

Ann. Statist., Volume 40, Number 5 (2012), 2601-2633.

First available in Project Euclid: 4 February 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62G20: Asymptotic properties

Local stationarity nonparametric regression smooth backfitting


Vogt, Michael. Nonparametric regression for locally stationary time series. Ann. Statist. 40 (2012), no. 5, 2601--2633. doi:10.1214/12-AOS1043.

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