On Equal Predictive Ability and Parallelism of Self-Exciting Threshold Autoregressive Model

Abstract

Several authors have developed statistical procedures for testing whether two models are similar. In this work, we not only present the notion of equivalence but also extend this to a measure of predictive ability of a time series following a stationary self-exciting threshold autoregressive (SETAR) process. A proposition and a lemma were used to join the structure of the predictability measure to the coefficients and sample autocorrelation of the SETAR process. Illustrative examples are given to show how to conduct the test which can help practitioners avoid mistakes in decision making.