In my work, I use the multivariate GARH model (DCC-GARCH). I am testing the existence of autocorrelation in the variance model. Ljung-Box tests (Q) for standardized residuals and square standardized residuals give different results.
Should I choose the Ljung-Box or Ljung-Box square test?
N=1500
See these links:
https://stats.stackexchange.com/questions/309917/ljung-box-test-for-squared-residuals-values-interpretation
https://www.statisticshowto.com/ljung-box-test/
https://www.rdocumentation.org/packages/portes/versions/5.0/topics/LjungBox
تستطيع الاعتماد على اختبار Ljung box لوحده في اختبار سلاسل البواقي للنموذج المقدر بالإضافة إلى اختبار جاركوا بيرا واختبارARCH متعدد المتغيرات
The Ljung-Box test is aimed at testing the independance of errors using residuals of an ARMA model estimated on the same data. But it makes use of autocorrelations so it is not powerful when the errors are uncorrelated but not independent. When applied to squared residuals, it can reveal ARCH and GARCH effects. Note that the errors of a ARCH-GARCH model are uncorrelated but not independent. Have a look at the excellent book by Francq and Zakoian entitled "GARCH Models: Structure, Statistical Inference and Financial Applications" published by Wiley in 2010.
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