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?