SIGNIFICANT VARIABLE SELECTION AND AUTOREGRESSIVE ORDER DETERMINATION FOR TIME‐SERIES PARTIALLY LINEAR MODELS

Abstract

This paper is concerned with the regression coefficient and autoregressive order shrinkage and selection via the smoothly clipped absolute deviation (SCAD) penalty for a partially linear model with time‐series errors. By combining the profile semi‐parametric least squares method and SCAD penalty technique, a new penalized estimation for the regression and autoregressive parameters in the model is proposed. We show that the asymptotic property of the resultant estimator is the same as if the order of autoregressive error structure and non‐zero regression coefficients are known in advance, thus achieving the oracle property in the sense of Fan and Li (2001). In addition, based on a prewhitening technique, we construct a two‐stage local linear estimator (TSLLE) for the non‐parametric component. It is shown that the TSLLE is more asymtotically efficient than the one that ignores the autoregressive time‐series error structure. Some simulation studies are conducted to illustrate the finite sample performance of the proposed procedure. An example of application on electricity usage data is also illustrated. Copyright © 2014 Wiley Publishing Ltd