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I have trouble understanding the output of the Ljung-Box test due to conflicting information:

The R documentation doesn't actually say how to interpret the output.

This site states that small p-values means that the data is likely to be stationary.

This otexts textbook states that large p-values means that the data is likely to be like white noise.

Clearly, one of them must be wrong. Which one is it?

Thanks!

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The first one is simply wrong. If you just check the wiki on L-B test, you will see that the null hypothesis is that the data are White Noise, so small $p$-values (say $<0.05$) mean that you have evidence to reject the null hypothesis. Here is a good online reference. Moreover, if you would like to test your data for white noise, in addition to this, I could suggest you try our hwwntest package which contains several types of white noise tests with examples.

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Both are correct because if we are doing the manual problem the p- value <0.05 means that we can accept the null hypothesis but in softwares such as SPSS and R if the p- value < 0.05 means that we can reject the null hypothesis because the table value which we used for manual problem is different for softwares.

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  • $\begingroup$ This sounds very surprising! Can you explain it better, or back it up with references? $\endgroup$
    – kjetil b halvorsen ♦
    Commented Apr 8, 2020 at 10:34

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