Chi‐squared portmanteau tests for structural VARMA models with uncorrelated errors

Abstract

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.