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Forecast covariances in the linear multiregression dynamic model
Author(s) -
Queen Catriona M.,
Wright Ben J.,
Albers Casper J.
Publication year - 2008
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.1050
Subject(s) - univariate , covariance , series (stratigraphy) , conditional variance , multivariate statistics , conditional independence , independence (probability theory) , mathematics , linear model , simple (philosophy) , econometrics , linear regression , covariance matrix , computer science , statistics , autoregressive conditional heteroskedasticity , volatility (finance) , paleontology , philosophy , epistemology , biology
The linear multiregression dynamic model (LMDM) is a Bayesian dynamic model which preserves any conditional independence and causal structure across a multivariate time series. The conditional independence structure is used to model the multivariate series by separate (conditional) univariate dynamic linear models, where each series has contemporaneous variables as regressors in its model. Calculating the forecast covariance matrix (which is required for calculating forecast variances in the LMDM) is not always straightforward in its current formulation. In this paper we introduce a simple algebraic form for calculating LMDM forecast covariances. Calculation of the covariance between model regression components can also be useful and we shall present a simple algebraic method for calculating these component covariances. In the LMDM formulation, certain pairs of series are constrained to have zero forecast covariance. We shall also introduce a possible method to relax this restriction. Copyright © 2008 John Wiley & Sons, Ltd.