Modeling covariance matrices via partial autocorrelations

JOURNAL OF MULTIVARIATE ANALYSIS

卷:100

Article

Daniels, M. J.¹  Pourahmadi, M.² 

[1] Univ Florida, Dept Stat, Gainesville, FL 32611 USA

[2] Texas A&M Univ, Dept Stat, College Stn, TX 77843 USA

关键词: Autoregressive parameters;    Cholesky decomposition;    Positive-definiteness constraint;    Levinson-Durbin algorithm;    Prediction variances;    Uniform and reference priors;    Markov chain Monte Carlo;   

DOI  :  10.1016/j.jmva.2009.04.015

来源: Elsevier

【 摘 要 】

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. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free