article

Modeling covariance matrices via partial autocorrelations

Authors:

M. PourahmadiAuthors Info & Claims

Journal of Multivariate Analysis, Volume 100, Issue 10

Pages 2352 - 2363

https://doi.org/10.1016/j.jmva.2009.04.015

Published: 01 November 2009 Publication History

Abstract

We study the role of partial autocorrelations in the reparameterization and parsimonious modeling of a covariance matrix. The work is motivated by and tries to mimic the phenomenal success of the partial autocorrelations function (PACF) in model formulation, removing the positive-definiteness constraint on the autocorrelation function of a stationary time series and in reparameterizing the stationarity-invertibility domain of ARMA models. It turns out that once an order is fixed among the variables of a general random vector, then the above properties continue to hold and follow from establishing a one-to-one correspondence between a correlation matrix and its associated matrix of partial autocorrelations. Connections between the latter and the parameters of the modified Cholesky decomposition of a covariance matrix are discussed. Graphical tools similar to partial correlograms for model formulation and various priors based on the partial autocorrelations are proposed. We develop frequentist/Bayesian procedures for modelling correlation matrices, illustrate them using a real dataset, and explore their properties via simulations.

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Cited By

Adametz DRoth V(2014)Distance-based network recovery under feature correlationProceedings of the 27th International Conference on Neural Information Processing Systems - Volume 110.5555/2968826.2968913(775-783)Online publication date: 8-Dec-2014
https://dl.acm.org/doi/10.5555/2968826.2968913
Wang YDaniels M(2014)Computationally efficient banding of large covariance matrices for ordered data and connections to banding the inverse Cholesky factorJournal of Multivariate Analysis10.1016/j.jmva.2014.04.026130(21-26)Online publication date: 1-Sep-2014
https://dl.acm.org/doi/10.1016/j.jmva.2014.04.026
Lee KLee JHagan JYoo J(2012)Modeling the random effects covariance matrix for generalized linear mixed modelsComputational Statistics & Data Analysis10.1016/j.csda.2011.09.01156:6(1545-1551)Online publication date: 1-Jun-2012
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Copyright © Elsevier Inc. © 2009.

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Academic Press, Inc.

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Publication History

Published: 01 November 2009

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Cited By

Adametz DRoth V(2014)Distance-based network recovery under feature correlationProceedings of the 27th International Conference on Neural Information Processing Systems - Volume 110.5555/2968826.2968913(775-783)Online publication date: 8-Dec-2014
https://dl.acm.org/doi/10.5555/2968826.2968913
Wang YDaniels M(2014)Computationally efficient banding of large covariance matrices for ordered data and connections to banding the inverse Cholesky factorJournal of Multivariate Analysis10.1016/j.jmva.2014.04.026130(21-26)Online publication date: 1-Sep-2014
https://dl.acm.org/doi/10.1016/j.jmva.2014.04.026
Lee KLee JHagan JYoo J(2012)Modeling the random effects covariance matrix for generalized linear mixed modelsComputational Statistics & Data Analysis10.1016/j.csda.2011.09.01156:6(1545-1551)Online publication date: 1-Jun-2012
https://dl.acm.org/doi/10.1016/j.csda.2011.09.011
Danaher PSmith M(2011)Rejoinder---Estimation Issues for Copulas Applied to Marketing DataMarketing Science10.1287/mksc.1100.060430:1(25-28)Online publication date: 1-Jan-2011
https://dl.acm.org/doi/10.1287/mksc.1100.0604
Carter CWong FKohn R(2011)Constructing priors based on model size for nondecomposable Gaussian graphical modelsJournal of Multivariate Analysis10.1016/j.jmva.2011.01.001102:5(871-883)Online publication date: 1-May-2011
https://dl.acm.org/doi/10.1016/j.jmva.2011.01.001

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