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 multisite streamflow generation and it is shown how these 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. 

In the concluding section, we summarize important practical implications for hydrologists.