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. In estimation and variable selection and for predicting the response variable with high accuracy, we propose the penalized method based on Smoothly Clipped Absolute Deviation Penalty (SCAD) in the sequential linear models. We conduct the simulations where the SCAD-penalized method is compared with other methods including the ordinary least squares (OLS), Lasso, and adaptive Lasso in the 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 data sets for further illustrating the performance of the SCAD-penalized method in the sequential linear modeling.