Modeling Covariance Matrices via Partial Autocorrelations. Academic Article

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 follows 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.

authors

• Pourahmadi, Mohsen

published proceedings

• J Multivar Anal

author list (cited authors)

• Daniels, M. J., & Pourahmadi, M.

citation count

• 57

complete list of authors

• Daniels, MJ||Pourahmadi, M

publication date

• January 2009

publisher

• Elsevier  Publisher

published in

• Journal of Multivariate Analysis  Journal

keywords

• Autoregressive Parameters
• Cholesky Decomposition
• Levinson-durbin Algorithm
• Markov Chain Monte Carlo
• Positive-definiteness Constraint
• Prediction Variances
• Uniform And Reference Priors

Digital Object Identifier (DOI)

• 10.1016/j.jmva.2009.04.015

start page

• 2352

end page

• 2363

volume

• 100

issue

• 10

URL

• http://dx.doi.org/10.1016/j.jmva.2009.04.015