Inference of time-varying regression models. (English) Zbl 1257.62049

Zhang, Ting; Wu, Wei Biao

Ann. Stat. 40, No. 3, 1376-1402 (2012).

Summary: 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.

MSC:

62G08	Nonparametric regression and quantile regression
62H15	Hypothesis testing in multivariate analysis
65C60	Computational problems in statistics (MSC2010)
62G20	Asymptotic properties of nonparametric inference
62G05	Nonparametric estimation
62G10	Nonparametric hypothesis testing

Keywords:

information criterion; locally stationary processes; nonparametric hypothesis testing; time-varying coefficient models; variable selection

Software:

fda (R)

References:

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