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

Year 2018, Volume: 31 Issue: 4, 1268 - 1282, 01.12.2018

Barış Asıkgıl

Abstract

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.

Keywords

Autocorrelation, Nonlinear time series, Self-exciting threshold autoregressive disturbances, Linear regression, Adapted two-stage least squares

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