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Multiregression dynamic models. (English) Zbl 0799.62097
Multidimensional non-Gaussian series are represented by one-dimensional dynamic linear models under some assumptions on conditional independence. The first step of modelling is to describe the causal relationships between the components of a time series by an influence diagram. Using a theorem of Pearl, Verma, Lauritzen et al. [see S. L. Lauritzen et al., Networks 20, No. 5, 491-505 (1990; Zbl 0743.05065)] it is shown that some conditional independence structures are preserved over time.
Two special cases are considered in which, besides exogenous variables, previous observations or preceding residuals as regressors are used. For these models the first two moments of the one-step-ahead forecasting distribution are calculated.

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)