An AdaptedApproach for Self-ExcitingThreshold Autoregressive Disturbances in Multiple Linear Regression

Abstract

Ordinary least squares method is usually used for parameter estimation in multiple linearregression models when all regression assumptions are satisfied. One of the problems inmultiple linear regression analysis is the presence of serially correlated disturbances. Serialcorrelation can be formed by autoregressive or moving average models. There are manystudies in the literature including parameter estimation in regression models especially withautoregressive disturbances. The motivation of this study is that whether serially correlateddisturbances are defined by a different type of nonlinear process and how this process isanalyzed in multiple linear regression. For this purpose, a nonlinear time series processknown as self-exciting threshold autoregressive model is used to generate disturbances inmultiple linear regression models. Two-stage least squares method used in the presence ofautoregressive disturbances is adapted for dealing with this new situation and comprehensiveexperiments are performed in order to compare efficiencies of the proposed method with theothers. According to numerical results, the proposed method can outperform under the typeof self-exciting threshold autoregressive autocorrelation problem when compared to ordinaryleast squares and two-stage least squares.