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Keywords:

  • VARMA models;
  • structural representation;
  • residual autocorrelation;
  • portmanteau test;
  • goodness-of-fit test

We consider portmanteau tests for testing the adequacy of structural vector autoregressive moving average models with uncorrelated errors. Under the assumption that errors are uncorrelated but non-independent, it is known that the Ljung–Box (or Box–Pierce) portmanteau test statistic is asymptotically distributed as a weighted sum of chi-squared random variables which can be far from the chi-square distribution usually employed. We therefore propose a new portmanteau statistic that is asymptotically chi-squared even in the presence of uncorrelated but non-independent errors. Monte Carlo experiments illustrate the finite sample performance for the proposed portmanteau test.