An Adapted Approach for Self-Exciting Threshold Autoregressive Disturbances in Multiple Linear Regression

Ordinary least squares method is usually used for parameter estimation in multiple linear regression models when all regression assumptions are satisfied. One of the problems in multiple linear regression analysis is the presence of serially correlated disturbances. Serial correlation can be formed by autoregressive or moving average models. There are many studies in the literature including parameter estimation in regression models especially with autoregressive disturbances. The motivation of this study is that whether serially correlated disturbances are defined by a different type of nonlinear process and how this process is analyzed in multiple linear regression. For this purpose, a nonlinear time series process known as self-exciting threshold autoregressive model is used to generate disturbances in multiple linear regression models. Two-stage least squares method used in the presence of autoregressive disturbances is adapted for dealing with this new situation and comprehensive experiments are performed in order to compare efficiencies of the proposed method with the others. According to numerical results, the proposed method can outperform under the type of self-exciting threshold autoregressive autocorrelation problem when compared to ordinary least squares and two-stage least squares.