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International Journal of Stochastic Analysis
Volume 2011 (2011), Article ID 151823, 20 pages
http://dx.doi.org/10.1155/2011/151823
Research Article

Yule-Walker Estimation for the Moving-Average Model

Department of Statistical Science, University College London, London WC1E 6BT, UK

Received 29 December 2010; Accepted 14 March 2011

Academic Editor: Qing Zhang

Copyright © 2011 Chrysoula Dimitriou-Fakalou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The standard Yule-Walker equations, as they are known for an autoregression, are generalized to involve the moments of a moving-average process indexed on any number of dimensions. Once observations become available, new moments estimators are set to imitate the theoretical equations. These estimators are not only consistent but also asymptotically normal for any number of indexes. Their variance matrix resembles a standard result from maximum Gaussian likelihood estimation. A simulation study is added to conclude on their efficiency.