Multivariate portmanteau test for autoregressive models with uncorrelated but nonindependent errors

Christian Francq, Hamdi Raïssi

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


We study the asymptotic behaviour of the least squares estimator, of the residual autocorrelations and of the Ljung-Box (or Box-Pierce) portmanteau test statistic for multiple autoregressive time series models with nonindependent innovations. Under mild assumptions, it is shown that the asymptotic distribution of the portmanteau tests is that of a weighted sum of independent chi-squared random variables. When the innovations exhibit conditional heteroscedasticity or other forms of dependence, this asymptotic distribution can be quite different from that of models with independent and identically distributed innovations. Consequently, the usual chi-squarcd distribution docs not provide an adequate approximation to the distribution of the Box-Pierce goodness-of-fit portmanteau test in the presence of nonindependent innovations. Hence we propose a method to adjust the critical values of the portmanteau tests. Monte carlo experiments illustrate the finite sample performance of the modified portmanteau test.

Original languageEnglish
Pages (from-to)454-470
Number of pages17
JournalJournal of Time Series Analysis
Issue number3
StatePublished - May 2007
Externally publishedYes


  • Box-pierce and Ljung-Box portmanteau tests
  • Diagnostic checking
  • Goodness-of-fit test
  • Residual autocorrelation
  • Vector weak AR model


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