Abstract.The paper describes model structures for representing multivariate time series containing stochastic trends and stochastic seasonal patterns. Methods for identification, fitting and checking these models are described. Two methods of identification are compared: using statistics calculated from (a) the unprewhitened stationary series, obtained by appropriately transforming and differencing the original series, (b) the series after prewhitening them by their univariate models. We see practical merit in using both methods of approach. A brief description is also given of the use of multivariate stochastic models for forecasting but a fuller description is to be given elsewhere, covering more general situations where the series may have to be aligned or phase‐shifted relative to each other to obtain a more parsimonious representatio
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