Modeling Covariance Matrices via Partial Autocorrelations.
Modeling Covariance Matrices via Partial Autocorrelations.
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DOI：
10.1016/j.jmva.2009.04.015
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发表时间：
2009-11-01
影响因子：
1.6
通讯作者：
Pourahmadi, M.
中科院分区：
文献类型：
--
作者：
Daniels, M. J.;Pourahmadi, M.
关键词：
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.
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