Modeling covariance matrices via partial autocorrelations

M.J. Daniels and M. Pourahmadi

Journal of Multivariate Analysis, 2009, vol. 100, issue 10, 2352-2363

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.

Keywords: Autoregressive; parameters; Cholesky; decomposition; Positive-definiteness; constraint; Levinson-Durbin; algorithm; Prediction; variances; Uniform; and; reference; priors; Markov; chain; Monte; Carlo (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (18)

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