Identification of multivariate time series and multivariate input‐output models

The problem of linear model structure identification for multivariate time series or multiple input‐output models is presented and solved. The identification is obtained using canonical correlations to determine model order. The equivalence between state‐space model structure and multivariate autoregressive moving average with exogenous inputs (ARMAX) models is presented. The class of models open to analysis includes rainfall‐runoff models, multivariate streamflow models, and time invariant state‐space models used in Kaiman filtering. Examples include a rainfall‐runoff model using three precipitation inputs, a four‐site monthly streamflow model, and a four‐season streamflow model.