Multivariate discount weighted regression and local level models

In this paper we propose a multivariate discount weighted regression technique to give a tractable solution to the problem of variance estimation and forecasting for the multivariate local level model. We give the correspondence between discount regression and matrix normal dynamic linear models and we show that the local level model can be treated with discount regression techniques. We illustrate the proposed methodology with London metal exchange data consisting of aluminium spot and future contract closing prices. The proposed estimate of the noise covariance matrix suggests these data exhibit high cross-correlation, which is discussed in some detail. The performance of the weighted regression model is evaluated with a simple outlier analysis. A sensitivity analysis shows that a low discount factor should be used and practical guidelines are given for general future use.