Multivariate discount weighted regression and local level models

The technique of multivariate discount weighted regression is used for forecasting multivariate time series. In particular, the discount regression model is modified to cater for the popular local level model for predicting vector time series. The proposed methodology is illustrated with London metal exchange data consisting of aluminium spot and future contract closing prices. The estimate of the measurement noise covariance matrix suggests that these data exhibit high cross-correlation, which is discussed in some detail. The performance of the proposed model is evaluated via an error analysis based on the mean of squared forecast errors, the mean of absolute forecast errors and the mean of absolute percentage forecast errors. A sensitivity analysis shows that a low discount factor should be used and practical guidelines are given for general future use.