Minimum message length order selection and parameter estimation of moving average models

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Abstract

This paper presents a novel approach to estimating a moving average model of unknown order from an observed time series based on the minimum message length principle (MML). The nature of the exact Fisher information matrix for moving average models leads to problems when used in the standard Wallace-Freeman message length approximation, and this is overcome by utilising the asymptotic form of the information matrix. By exploiting the link between partial autocorrelations and invertible moving average coefficients an efficient procedure for finding the MML moving average coefficient estimates is derived. The MML estimating equations are shown to be free of solutions at the boundary of the invertibility region that result in the troublesome "pile-up" effect in maximum likelihood estimation. Simulations demonstrate the excellent performance of the MML criteria in comparison to standard moving average inference procedures in terms of both parameter estimation and order selection, particularly for small sample sizes.

Original languageEnglish
Title of host publicationAlgorithmic probability and friends
Subtitle of host publicationBayesian prediction and artificial intelligence - papers from the Ray Solomonoff 85th memorial conference
PublisherSpringer
Pages327-338
Number of pages12
ISBN (Print)9783642449574
DOIs
Publication statusPublished - 2013
Externally publishedYes
EventRay Solomonoff 85th Memorial Conference on Algorithmic Probability and Friends: Bayesian Prediction and Artificial Intelligence - Melbourne, VIC, Australia
Duration: 30 Nov 20112 Dec 2011

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume7070
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceRay Solomonoff 85th Memorial Conference on Algorithmic Probability and Friends: Bayesian Prediction and Artificial Intelligence
CountryAustralia
CityMelbourne, VIC
Period30/11/112/12/11

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