Exploring finite mixtures of Gaussian Innovations in ARX(1) Model

Abstract

Researchers have introduced and studied AR(1) model with explanatory variable to model a variety of time series data. A usual assumption in these models is that the innovations follow a single gaussian distribution. There might occur situations in which errors in the model may arise from several subpopulations rather than a single density. In this study a mixture distribution to model the innovations in an AR(1) Model with Explanatory variable has been introduced. A simulation study has been conducted to justify the proposed theory. An Empirical analysis on real time data set has also been conducted to provide application.