  We investigate the optimal structure of dynamic regression models used in
multivariate time series prediction and propose a scheme to form the lagged
variable structure called Backward-in-Time Selection (BTS) that takes into
account feedback and multi-collinearity, often present in multivariate time
series. We compare BTS to other known methods, also in conjunction with
regularization techniques used for the estimation of model parameters, namely
principal components, partial least squares and ridge regression estimation.
The predictive efficiency of the different models is assessed by means of Monte
Carlo simulations for different settings of feedback and multi-collinearity.
The results show that BTS has consistently good prediction performance while
other popular methods have varying and often inferior performance. The
prediction performance of BTS was also found the best when tested on human
electroencephalograms of an epileptic seizure, and to the prediction of returns
of indices of world financial markets.
