The behaviour of the Lagrangian multiplier test in testing the orders of an ARMA-model

Summary The Lagrange multiplier test for testing the order of an ARMA-model is investigated. It is shown that it exhibits some pathologies stemming from the special properties of parameter spaces of ARMA-models. As a consequence one has to be careful in using the LM-test in this context. Furthermore results of this paper are used in a subsequent paper [Pötscher, 1983], to show the consistency of an order estimation procedure based on Lagrange multiplier tests, described there.