This paper provides an extension of the application of score, or Lagrangian multiplier, tests to diagnostic checking of ARMA, autoregressive-moving average, models. The score test procedure for testing the null hypothesis of an ARMA( p,q ) process against certain ARMA ( p⊞r, q⊞s ) alternatives is considered and shown to be of the form of a pure significance test.
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Poskitt et al. (1980) studied this question.
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