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Model and variable selection procedures for semiparametric time series regression. (English) Zbl 1201.62101

Summary: Semiparametric regression models are very useful for time series analysis. They facilitate the detection of features resulting from external interventions. The complexity of semiparametric models poses new challenges for issues of nonparametric and parametric inference and model selection that frequently arise from time series data analysis. We propose penalized least squares estimators which can simultaneously select significant variables and estimate unknown parameters. An innovative class of variable selection procedure is proposed to select significant variables and basis functions in a semiparametric model. The asymptotic normality of the resulting estimators is established. Information criteria for model selection are also proposed. We illustrate the effectiveness of the proposed procedures with numerical simulations.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
65C60 Computational problems in statistics (MSC2010)
62F10 Point estimation
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