2.10 "Testing For serial correlation", presents a unified theoretical analysis, and I believe, clarifies the matter. Some power studies of a portmanteau test of time series model specification. Maddala also mentions the low power of the test, see for example Davies, N., & Newbold, P. Maddala's argument against the Ljung-Box test is the same as the one raised against another omnipresent autocorrelation test, the "Durbin-Watson" one: with lagged dependent variables in the regressor matrix, the test is biased in favor of maintaining the null hypothesis of "no-autocorrelation" (the Monte-Carlo results obtained in answer allude to this fact). Maddala literally laments the widespread use of this test, and instead considers as appropriate the "Langrange Multiplier" test of Breusch and Godfrey. with lagged dependent variables in the regressor matrix), see particularly Maddala (2001) "Introduction to Econometrics (3d edition), ch 6.7, and 13. There are some strong voices in the Econometrics community against the validity of the Ljung-Box $Q$-statistic for testing for autocorrelation based on the residuals from an autoregressive model (i.e.
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