Fast same-step forecast in SUTSE model and its theoretical properties

We consider the problem of forecasting multivariate time series by a Seemingly Unrelated Time Series Equations (SUTSE) model. The SUTSE model usually assumes that error variables are correlated. A crucial issue is that the model estimation requires heavy computational loads because of a large matrix computation, especially for high-dimensional data. To alleviate the computational issue, we propose a two-stage procedure for forecasting. First, we perform the Kalman filter as if error variables are uncorrelated; that is, univariate time-series analyses are conducted separately to avoid a large matrix computation. Next, the forecast value is computed by using a distribution of forecast error. The proposed algorithm is much faster than the ordinary SUTSE model because we do not require a large matrix computation. Some theoretical properties of our proposed estimator are presented. Monte Carlo simulation is performed to investigate the effectiveness of our proposed method. The usefulness of our proposed procedure is illustrated through a bus congestion data application.