Ljung-Box Q-test result variation

Question

I am conductin Ljung-Box tests to test the autocorrelation/serial correlation of a variable. My results confuse me a little bit and I don't really know what to conclude from them. For q = 1,2,3 (number of lags considered when calculating the test statistic) I can reject the null hypothesis of no autocorrelation. For q=4:11 I cannot reject the null and q=12,13 I can reject again.

From my point of view the power of the test should increase as I reduce q (number of lags considered when calculating the test statistic). Is this incorrect?

What would you conclude from these results? Am I doing something wrong?

Answer 1

You are not necessarily doing anything wrong. Imagine there is actual autocorrelation at lags 1 and 12. You find it with LB(1). You still find it with LB(2) and LB(3), but the results are less strong as the test statistic gets diluted by the non-autocorrelated lags 2 and 3. When they get diluted further, the results become insignificant (lags 4 to 11). But then you reach lag 12, the autocorrelation at lags 1 and 12 are again strong enough so as not to get diluted to the level of insignificance in LB(12). So you get a significant result there and similarly for LB(13).

This is just one example. You could come up with something similar with other combinations of autocorrelated and non-autocorrelated lags.