Variable selection for single-index-driven autoregressive model with linear explanatory variables

Linear time series models are useful tools to analyse times series data which is collected over time. However, they are not sufficient and powerful to deal with time series data with nonlinear features, and nonlinear time series models are required to be explored. In this paper, we investigate the problem of variable selection for single-index-driven autoregressive model with linear explanatory variables, which is one of the nonlinear forms. The procedure based on the local linear method and the penalized least squares method can select the significant parametric components and estimate the unknown parameter simultaneously. Besides, the iterative algorithm to construct the local estimator for unknown function and the penalized estimator for unknown parameter is presented. Moreover, the asymptotic normality of the local linear estimator, together with the consistency and the oracle property of the penalized least squares estimator are established. Finally, some simulation studies and a real data example are conducted to illustrate the finite sample behaviour of the variable selection method.