An Approach to Testing Linear Times Series Models

Abstract

The purpose of this paper is to develop diagnostic tests for open-loop transfer function models with autoregressive-moving average stochastic disturbances using the efficient scores procedure. The tests proposed are asymptotically equivalent to those based upon the likelihood ratio principle and have the advantage that they do not involve a heavy computational burden. Consideration is given both to the standard case of nonsingular information matrices and to the situation obtaining when there are identifiability problems and application of conventional large sample test procedures is not feasible. Relationships between score tests and portmanteau tests in time series analysis are also investigated. Some simulation evidence on the finite sample behaviour of the tests is presented and it is seen that the tests of this paper perform well.