The analysis of multivariate time series applied to problems in hydrology

In this paper we discuss stochastic models for vector processes, in particular the class of multivariate autoregressive moving average models. Special cases of this class have been discussed in the literature on synthetic hydrology and it is shown how these results can be brought into a general framework. An iterative model building procedure, consisting of model specification — estimation — diagnostic checking is stressed. Results on model specification are given and it is shown how partial autocovariance matrices can be used to check whether multivariate autoregressive models provide adequate representation for (standardized) streamflow sequences. Furthermore, estimation of parameters in multivariate autoregressive moving average models is discussed and it is pointed out that moment estimators can be inefficient when moving average parameters are present. An approximate maximum likelihood estimation procedure is suggested. Furthermore, an inconsistency in modelling hydrologic sequences is pointed out; it is shown that in general it is not possible to have the individual series in a multivariate (first-order) autoregressive process follow univariate processes of the same (first) order.

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