Parameter estimation of regression model with AR(p) error terms based on skew distributions with EM algorithm

Abstract

Parameter estimation and the variable selection are two pioneer issues in regression analysis. While traditional variable selection methods require prior estimation of the model parameters, the penalized methods simultaneously carry on parameter estimation and variable select. Therefore, penalized variable selection methods are of great interest and have been extensively studied in literature. However, most of the papers in literature are only limited to the regression models with uncorrelated error terms and normality assumption. In this study, we combine the parameter estimation and the variable selection in regression models with autoregressive error term by using different penalty functions under heavy tailed error distribution assumption. We conduct a simulation study and a real data example to show the performance of the estimators.

Empirical likelihood estimation for linear regression models with AR(p) error terms with numerical examples

“…In literature, parameters of an autoregressive error term regression model are estimated using LS, ML or CML estimation methods. Some of the related papers are [1], [3], [24], [25] and [26]. In all of the mentioned papers some known distributions, such as normal or t, are assumed as the error distribution to carry on estimation of the parameters of interest in this model.…”

Skew Generalized Normal Innovations for the AR(p) Process Endorsing Asymmetry

“…Bondon [5] and, more recently, Sharafi and Nematollahi [6] and Ghasami et al [7] considered AR models defined by the epsilon-skew-normal (E SN ), skew-normal (S N ), and generalized hyperbolic (GH) innovation processes, respectively. Finally, AR models are not only applied in the time series environment: Tuaç et al [8] considered AR models for the error terms in the regression context, allowing for asymmetry in the innovation structures.…”