Diagnostic tests for multiple time series models

This paper is concerned with the development and application of diagnostic checks for vector linear time series models. A hypothesis testing procedure based upon the score, or Lagrangean multiplier, principle is advocated and the distributions of the test statistic both under the null hypothesis and under a Pitman sequence of alternatives are discussed. Consideration of alternative models with singular sensitivity matrices when the null hypothesis is true leads to an interpretation of the score test as a pure significance test and to a notion of an equivalence class of local alternatives. Portmanteau tests of model adequacy are also investigated and are seen to be equivalent to score tests.