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My data are 6 variables × 68 data. Null hypothesis is there is no serial correlation. Is p=0.13 too small? it is very close to 0.1. The significance level I choose is 0.05 though.

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    $\begingroup$ You do not really accept 'the absence of correlation' but rather not reject it. What you could test and accept is whether the correlation is below a certain level. $\endgroup$
    – Sextus Empiricus
    Commented Aug 21, 2019 at 6:59

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This strongly depends on the consequences of a serial correlation for following line of actions. If this is meant as a test of an independence assumption, I can tell you that typically, already minor dependencies (e.g., an intra-class correlation of 0.05 für linear models) can cause severely distorted inferences. Therefore, 0.1 may already be large enough to cause concern.

Otherwise, I think, you should give more context on what you are actually doing so that one can suggest an appropriate procedure to infer if a sample value of 0.1 is enough evidence for the null hypothesis.

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  • $\begingroup$ I conducted a serial correlation as the last step of a diagnostic test for my VECM model. I also conducted a heteroskedasticity test (another diagnostic test), and the p-value is 0.49, also a no rejection of the null, and there is no heteroskedasticity. So I just want to make sure if there is a serial correlation. If 0.13 is ok for a no rejection, it marks the end of the analysis, and the results of VECM are accepable, otherwise, I will need to choose other lags and re-run the model. $\endgroup$
    – Elizabeth
    Commented Aug 21, 2019 at 6:30
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    $\begingroup$ Well, then I would do some research to find out what is the maximum acceptable level of serial correlation (I am not an expert on this specific model.) and test if your correlation is smaller or equal than that (as suggested by the commenter above). But: If I were in your position, I would do the rerun with different lags anyway just to get a glimpse of how robust my results are. $\endgroup$
    – StoryTeller0815
    Commented Aug 21, 2019 at 14:06

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