A generalized Burr mixture autoregressive models for modeling non linear time series

Abstract

A more flexible type of mixture autoregressive model, namely the Burr mixture autoregressive, BMAR model is studied in this article for modeling non linear time series. The model consists of a mixture of K autoregressive components with each conditional distribution of the component following a Burr distribution. The BMAR model enjoys some nice statistical properties which allow it to capture time series with: (1) unimodal or multimodal; (2) asymmetry or symmetry conditional distribution; (3) conditional heteroscedasticity; (4) cyclical or seasonal; and (5) conditional leptokurtic distribution. Sufficient and less restrictive conditions for the ergodicity of the BMAR model are derived and discussed. A more robust constrained optimization algorithm (EM – sequential quadratic programming method) is proposed for the non linear optimization problem. From the simulation studies carried out, the parameters estimation method showed satisfying results. The variance of the estimated parameters is also addressed with the missing information principle. Real datasets from two different fields of study are used to assess the performance of the BMAR model compared to other competing models. The comparison done in the empirical examples reveals the supremacy of the BMAR model in capturing the data behavior.