Specification and Checking the Adequacy of VARMA Models

A great number of strategies has been suggested for specifying VARMA models. There is not a single one that has become a standard like the Box & Jenkins (1976) approach in the univariate case. None of the multivariate procedures is in widespread use for modelling moderate or high-dimensional economic time series. Some are mainly based on a subjective assessment of certain characteristics of a process such as the autocorrelations and partial autocorrelations. A decision on specific orders and constraints on the coefficient matrices is then based on these quantities. Other methods rely on a mixture of statistical testing, use of model selection criteria and personal judgement of the analyst. Again other procedures are based predominantly on statistical model selection criteria and, in principle, they could be performed automatically by a computer. Automatic procedures have the advantage that their statistical properties can possibly be derived rigorously. In actual applications, some kind of mixture of different approaches is often used. In other words, the expertise and prior knowledge of an analyst will usually not be abolished in favor of purely statistical procedures. Models suggested by different types of criteria and procedures will be judged and evaluated by an expert before one or more candidates are put to a specific use such as forecasting. The large amount of information in a number of moderately long time series makes it usually necessary to condense the information considerably before essential features of a system become visible.