Fitting MA(q) Models in the Closed Invertible Region

TL;DR

This paper discusses reparameterization techniques for MA(q) models, introduces a method to test boundary estimates, and demonstrates that boundary estimates become more common as q increases through simulation results.

Contribution

It presents a general testing method for boundary estimates in MA(q) models and explores how boundary estimates prevalence increases with model order q.

Findings

Boundary estimates probability increases with q

Reparameterization aids likelihood maximization

Test effectively detects boundary estimates

Abstract

The use of reparameterization in the maximization of the likelihood function of the MA(q) model is discussed. A general method for testing for the presence of a parameter estimate on the boundary of an MA(q) model is presented. This test is illustrated with a brief simulation experiment for the MA(q) for q=1,2,3,4 in which it is shown that the probability of an estimate being on the boundary increases with q.