Learning algorithm for selection of an autoregressive model for multi-step ahead forecast

The paper addresses the problem of learning an order of an autoregressive (AR) model with multi step ahead prediction properties and describes a computational learning algorithm based on a new selection criterion (“pattern residuals´ interdependence measure estimator”-PRIME). The PRIME criterion for the selection of an AR model with sufficient predictive power measures interdependence among residuals obtained from a given training set (an observed time series), a time series modelled by an autoregressive moving average (ARMA) process, and a corresponding deterministic pattern extracted from the original data by a smoothing filter. As a measure of the residuals´ interdependence, a mean expected log likelihood function of a correlation coefficient between the residuals is defined. The paper presents the results of Monte Carlo simulation which generate an empirical distribution of the proposed estimator and provide evidence of appropriate identification of data. It illustrates also the results obtained by multi step ahead forecast for actual data. The comparison between models selected by the proposed criterion and well known criteria provides favourable evidence for the strength of the PRIME criterion