The Annals of Statistics

Inference of time-varying regression models

Ting Zhang and Wei Biao Wu

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We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate processes. With a two-stage method, the parametric component can be estimated with a $n^{1/2}$-convergence rate. A simulation-assisted hypothesis testing procedure is proposed for testing significance and parameter constancy. We further propose an information criterion that can consistently select the true set of significant predictors. Our method is applied to autoregressive models with time-varying coefficients. Simulation results and a real data application are provided.

Article information

Ann. Statist., Volume 40, Number 3 (2012), 1376-1402.

First available in Project Euclid: 10 August 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62G10: Hypothesis testing
Secondary: 62G20: Asymptotic properties

Information criterion locally stationary processes nonparametric hypothesis testings time-varying coefficient models variable selection


Zhang, Ting; Wu, Wei Biao. Inference of time-varying regression models. Ann. Statist. 40 (2012), no. 3, 1376--1402. doi:10.1214/12-AOS1010.

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