JOINT DETERMINATION OF AUTOREGRESSIVE ORDER AND DEGREE OF DIFFERENCING

Abstract

Box and Jenkins (1970) consider a method of building ARIMA(p,d,q) models to describe the behaviour of an observed time series. The basic idea is to describe the underlying stochastic structure parsimoniously but adequately. Model adequacy, among other things, means that the model transforms the data into white noise. Powerful white noise tests are of importance in practical time series analysis. In this paper we present an objective method to build ARI(p,d) models. The approach follows the model building principles of Box and Jenkins; find a parsimoniously parametrized model which transforms the data into white noise. The white noise hypothesis is tested by applying an autoregressive order determination criterion for the residuals. This approach leads to a new order determination criterion. Its statistical properties are illustrated with simulations. The method is also compared with traditional order determination methods.