Model and Variable Selection Procedures for Semiparametric Time Series Regression

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.

Remote sensing‐based retrieval of soil moisture content using stacking ensemble learning models

“…The relationship between the factors influencing SMC is not linear. Most of the influencing factors can easily have synergistic or inhibitory effects on soil moisture retrieval if they are not screened, reducing the retrieval efficiency of the algorithm (Kato & Shiohama, 2009). Chen et al (2020) report that a good feature set should contain a few features and contribute to improving model accuracy.…”

“…Most of the influencing factors can easily have synergistic or inhibitory effects on soil moisture retrieval if they are not screened, reducing the retrieval efficiency of the algorithm (Kato & Shiohama, 2009). Chen et al (2020) score.…”

Variable Selection in Nonparametric and Semiparametric Regression Models

“…Ni, Zhang, and Zhang (2009) propose a doublepenalized least squares (DPLS) approach to simultaneously achieve the estimation of the nonparametric component  and the selection of important variables in   in (4.1). Kato and Shiohama (2009) consider variable selection in (4.1) in the time series framework. In the large  framework, Chen, Yu, Zou, and Liang (2012) propose to use the adaptive Elastic-net for variable selection for parametric components by using profile least squares approach to convert the partially linear model to a classical linear regression model.…”

“…In the case where  =   is divergent with   ¿  they also establish the selection consistency by allowing the number  *  of nonzero components in  to be divergent at a slow rate. Kato and Shiohama (2009) consider the PLM in (4.1) in the time series framework by restricting   =   =  and allowing   to be a linear process. They assume that  (  ) is an unknown time trend function that can be exactly expressed as…”

Semiparametric Time-Series Model Using Local Polynomial: An Application on the Effects of Financial Risk Factors on Crop Yield

“…Moreover, interpretation of the semiparametric model is easy and understandable. Some of the important studies on the semiparametric time series model are as follows: Kato and Shiohama (2009), Gao and Phillips (2010), and Aydın and Yılmaz (2021). These studies used kernel and spline-based estimators and applied these estimators to different application fields including econometrics, censored time-series data and medical applications.…”