Modeling Covariance Matrices via Partial Autocorrelations. Academic Article uri icon

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.

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 1, 2009 11:11 AM