I am a beginner at ARIMA model fitting. I have observed that after I fit my model, the Ljung-Box statistic tend to discard the null hypothesis for large lag. It could be that it is only random that it happened on every data set I have tried, but it tends to be so frequent that I am starting to believe there is a mechanism that causes it.

If this is a somewhat general finding, I would be curious to learn the answer to the following two questions:

  1. How do I determine how large lag I should restrict my attention to. I see 20 is a common value, but no one has explained why.
  2. Is there a limited number of effects that causes the p-values to decrease as the lag decreases? Could we anticipate this behaviour somehow?

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