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I'm working with the "rugarch" package in R. This package provides the weighted Ljung-Box test for the standardized residuals and for the standardized squared residuals. What are the null hypothesis of both of these tests?

I couldn't understand the explanation provided in the vignette. I also tried to figure out from the article in the references, but I'm new on working with GARCH models, so I couldn't understand much of it. Can anyone tell me in a simple way what are the null hypothesis?

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  • $\begingroup$ I think we need more about what you do understand and what you do not. $\endgroup$ – mdewey Feb 11 '17 at 16:45
  • $\begingroup$ I know what's the purpose of the original Ljung-Box test. The package tells me that H0 for the weighted Ljung-Box test for standardized residuals is "no serial correlation", and I can understand that. My problem is with the weighted Ljung-Box test for standardized squared residuals. I don't know what's its null hypothesis. I searched on the vignette and it only tells about the first test, not the last. I need to understand the use of this test, because it keeps returning p-values of 0, which is not appropriate, I guess.. Anyway, I just want to understand what is this test for. $\endgroup$ – Luis Novoa Feb 11 '17 at 17:18
  • $\begingroup$ I was going through my old answers and noticed this one was not accepted. Do you perhaps need further clarification? $\endgroup$ – Richard Hardy Feb 28 '17 at 15:18
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The weighted Ljung-Box test has the same null hypothesis as the regular Ljung-Box test. The weighting only helps to increase the power of the test, but it does not change the null hypothesis. You can read more about this in the papers that the "rugarch" manual references to.

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