Generating random AR(p) and MA(q) Toeplitz correlation matrices

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Generating random AR(p) and MA(q) Toeplitz correlation matrices

TitleGenerating random AR(p) and MA(q) Toeplitz correlation matrices
Publication TypeJournal Article
Year of Publication2010
AuthorsNg, CT, Joe, H
JournalJournal of Multivariate Analysis
Volume101
Pagination1532-1545
Date PublishedJUL
Type of ArticleArticle
ISSN0047-259X
KeywordsAutoregressive process, Beta distribution, Longitudinal data, Moving average process
AbstractMethods are proposed for generating random (p+1) x (p+1) Toeplitz correlation matrices that are consistent with a causal AR(p) Gaussian time series model. The main idea is to first specify distributions for the partial autocorrelations that are algebraically independent and take values in (-1, 1), and then map to the Toeplitz matrix. Similarly, starting with pseudopartial autocorrelations, methods are proposed for generating (q+1) x (q+1) Toeplitz correlation matrices that are consistent with an invertible MA(q) Gaussian time series model. The density can be uniform or non-uniform over the space of autocorrelations up to lag p or q, or over the space of autoregressive or moving average coefficients, by making appropriate choices for the densities of the (pseudo)-partial autocorrelations. Important intermediate steps are the derivations of the Jacobians of the mappings between the (pseudo)-partial autocorrelations, autocorrelations and autoregressive/moving average coefficients. The random generating methods are useful for models with a structured Toeplitz matrix as a parameter. (C) 2010 Elsevier Inc. All rights reserved.
DOI10.1016/j.jmva.2010.01.013