Margin-closed vector autoregressive time series models
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Conditions are obtained for a Gaussian vector autoregressive time series of order k, VAR(k), to have univariate margins that are autoregressive of order k or lower-dimensional margins that are also VAR(k). This can lead to d-dimensional VAR(k) models that are closed with respect to a given partition {S_1,…,S_n} of {1,…,d} by specifying marginal serial dependence and some cross-sectional dependence parameters. The special closure property allows one to fit the sub-processes of multivariate time series before assembling them by fitting the dependence structure between the sub-processes. We revisit the use of the Gaussian copula of the stationary joint distribution of observations in the VAR(k) process with non-Gaussian univariate margins but under the constraint of closure under margins. This construction allows more flexibility in handling higher-dimensional time series and a multi-stage estimation procedure can be used. The proposed class of models is applied to a macro-economic data set and compared with the relevant benchmark models.
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