Variable Selection in Semi-Functional Partially Linear Regression Models with Time Series Data

This article investigates a variable selection method in semi-functional partially linear regression (SFPLR) models for strong $\alpha$-mixing functional time series data. We construct penalized least squares estimators for unknown parameters and unknown link functions in our models. Under some regularity assumptions, we establish the asymptotic convergence rate and asymptotic distribution for the proposed estimators. Furthermore, we make a comparison of our variable selection method with the oracle method without variable selection in simulation studies and an electricity consumption data analysis. Simulation experiments and real data analysis results indicate that the variable selection method performs well at extracting the primary information and reducing dimensionality.