Estimation of linear filter banks for multivariate time series prediction with temporal principal component analysis

We present an automated estimation procedure for linear filter banks. The motivation for such an automated design procedure comes from developments in the application of neural networks to time series prediction and modelling. The estimation procedure is based on neural implementation of the Karhunen-Loeve transform. FIR filters are obtained through computation of a principal component transform (PCA) on tapped-delay lines of a time series. The FIR filter output is used to predict the time series with a feedforward neural network. The results of the proposed method are compared to other focused time lagged neural networks: the tapped-delay line neural network and the Gamma network. The three techniques are compared by focusing capacities, speed of convergence, quality of prediction and efficiency i.e. ratio of prediction quality and memory usage. The temporal PCA method outperforms the ordinary TDL-network slightly considering prediction error, the Gamma network however is not beaten, provided that the number of taps is not over-estimated. Gamma filters appear to be more efficient as they achieve large time-scopes with a small number of taps. Adaptive Gamma filters seem to be the more promising technique for automated design of focusing filters for neural time series prediction.