Statistical techniques for time series clustering and classification are often necessary to provide useful information for the solution of real problems arising from different domains. For this reason, the study of distance measures and discriminating rules for time series has represented an important area of research in several scientific fields. In this article, the statistical properties of the autoregressive (AR) distance between ARIMA processes are investigated. In particular, the asymptotic distribution of the squared AR distance and an approximation which is computationally efficient are derived. Moreover, the problem of time series clustering and classification is discussed and the performance of the AR distance is illustrated by means of some empirical applications.