کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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1146814 | 1489695 | 2009 | 12 صفحه PDF | دانلود رایگان |

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.
Journal: Journal of Multivariate Analysis - Volume 100, Issue 10, November 2009, Pages 2352–2363