Estimation and Variable Selection in Sequential Linear Models: SCAD-Penalized Method with Applications

Sequential linear models can be adopted to describe the data where the response variable depends on lagged outcomes and fixed-effects variables. For estimation, variable selection, and high-accuracy response prediction, we propose the penalized method based on the Smoothly Clipped Absolute Deviation Penalty (SCAD) for sequential linear models. We conduct simulations comparing the SCAD-penalized method with ordinary least squares (OLS), Lasso, and adaptive Lasso in sequential linear models. The simulation results demonstrate that the SCAD-penalized method in the sequential linear models excels in estimation with better accuracy and precision and in variable selection with better prediction. We apply the proposed method to two real datasets to further illustrate the performance of the SCAD-penalized method in sequential linear modeling.