Abstract
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. In this paper, 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.
Highlights
Non- and semiparametric regression has become a rapidly developing field of statistics in recent years
A major problem associated with non- and semiparametric trend estimation involves the selection of a smoothing parameter and the number of basis functions
In this article we have proposed variable and model selection procedures for the semiparametric time series regression
Summary
Non- and semiparametric regression has become a rapidly developing field of statistics in recent years. Most literature on nonparametric regression with dependent errors focuses on the kernel estimator of the trend function see, e.g., Altman 1 , Hart 2 and Herrmann et al 3. These results have been extended to the case with long-memory errors by Hall and Hart 4 , Ray and Tsay 5 , Journal of Probability and Statistics and Beran and Feng 6. Variable selection of the smoothing parameter for the basis functions is important problem in non- and semiparametric models. Several information criteria for evaluating models constructed by various estimation procedures have been proposed, see, for example, Konishi and Kitagawa.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have