  A new test is proposed for the weak white noise null hypothesis. The test is
based on a new automatic choice of the order for a Box-Pierce or Hong test
statistic. The test uses Lobato (2001) or Kuan and Lee (2006) HAC critical
values. The data-driven order choice is tailored to detect a new class of
alternatives with autocorrelation coefficients which can be $o(n^{-1/2})$
provided there are enough of them. A simulation experiment illustrates the good
behavior of the test both under the weak white noise null and the alternative.
