I'm interested into the Portmanteau tests for fitting ARIMA models and ended up to Ljung-Box test and their implementations for R-statistics. I've read already some relative question on the subject and came to the conclusion that the safest way to reject the null hypothesis is when p<0.05. However I was browsing this site, where the author gets the following results for the test and h=20:

X-squared = 13.5844, df = 20, p-value = 0.851

and states that: "*and the p-value for the Ljung-Box test is 0.9, we can conclude that there is very little evidence for non-zero autocorrelations in the forecast errors at lags 1-20*"

What am I missing here?

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#### Best Answer

I don't think you are missing anything. With 20 d.f., the critical value at the .05 level is 31.41.

13.58 is less than that, so the hypothesis that there is no meaningful autocorrelation is not rejected.

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