An unified approach to model selection, discrimination, goodness of fit and outliers in time series

Abstract

This article presents an unified approach of several procedures in time series. First, we show that quadratic discrimination provides a unifying approach for deriving model selection criteria in the ARMA framework. Second, we establish a connection between model selection criteria and a goodness of fit test. Finally, we show that the outlier detection problem can be seen as a particular case of model selection. Therefore, the problems of model selection, discrimination, goodness of fit tests and outliers can be treated under the same principles.