Estimating Moving Average Processes with an improved version of Durbin's Method

TL;DR

This paper introduces an improved method for estimating univariate and multivariate moving average processes, extending Durbin's approach to handle both invertible and non-invertible cases, including unit root processes.

Contribution

It presents a simple, recursive estimation technique applicable to a wider class of MA processes, including unstable and non-invertible ones, under specific initial conditions.

Findings

Method works for invertible and non-invertible MA processes.

Applicable to processes with unit roots.

Provides a recursive relation between MA and AR parameters.

Abstract

This paper provides a simple method to estimate both univariate and multivariate MA processes. Similar to Durbin's method, it rests on the recursive relation between the parameters of the MA process and those of its AR representation. This recursive relation is shown to be valid both for invertible / stable and non invertible / unstable processes under the assumption that the process has no constant and started from zero. This makes the method suitable for unit root processes, too.