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

Abstract

The problem of forecasting multivariate time series by a Seemingly Unrelated Time Series Equations (SUTSE) model is considered. 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, a two-stage procedure for forecasting is constructed. First, Kalman filtering is performed as if the 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 a large matrix computation is not required. Some theoretical properties of the proposed estimator are presented, and Monte Carlo simulation is performed to investigate the effectiveness of the proposed method. The usefulness of the proposed procedure is illustrated through a bus congestion data application.