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Multivariate Portmanteau Test For Autoregressive Models with Uncorrelated but Nonindependent Errors
Author(s) -
Francq Christian,
Raïssi Hamdi
Publication year - 2007
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2006.00521.x
Subject(s) - mathematics , heteroscedasticity , autoregressive model , estimator , asymptotic distribution , test statistic , independent and identically distributed random variables , econometrics , statistics , series (stratigraphy) , statistical hypothesis testing , random variable , paleontology , biology
. 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‐squared distribution does 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.