AbstractThe purposes of this paper are to introduce a multivariate non‐stationary stochastic time series model without individual detrending and to extract the multiple relationships between variables. To infer the statistical relation between variables, we attempt to estimate the co‐movement of multivariate non‐stationary time series components. The model is expressed in state‐space form, and time series components are estimated by the maximum likelihood method using numerical optimization algorithm. The Kalman filter algorithm is used to compute the likelihood of the model. The AIC procedure gives a criterion for selecting the best model fit for the data. The multiple relationship becomes clear by analysing estimated AR coefficients. Real economic data are used for a numerical