Predictions in time series using multivariate regression models (Q2740041)

There are many possibilities for prediction of time series. The well-known and commonly used are methods based on the Box-Jenkins methodology [\textit{G.E.P. Box} and \textit{G.M. Jenkins}, Time series analysis forecasting and control. (1970; Zbl 0249.62009)]. The other approach is based on modeling time series by regression models and finding the best linear unbiased predictor (BLUP). This method is known in the engineering literature as ``kriging''.NEWLINENEWLINENEWLINEThe aim of this paper is to study a method of prediction using multivariate regression models. The method is based on the idea of predicting future values of an observed time series using multivariate regression models with estimated and predicted regression parameters. It is known that this approach can be studied by the methods of kriging for finding the BLUPs of future observations. The BLUPs are derived by using Kronecker products of matrices and their basic properties. Predictions are studied w.r.t. their mean squared errors.NEWLINENEWLINENEWLINETwo methods of prediction are proposed: the simple one and the above-mentioned method based on kriging theory. The mean squared errors of these predictions are computed and it is shown that the first one can be regarded as a special case of the kriging approach.