The perils of inferring serial dependence from sample autocorrelations of moving average series

We demonstrate that oscillatory patterns in the higher lags of sample autocorrelations can arise whenever the true process is a finite order MA, and that this phenomenon exists even when the true autocorrelations are zero. Therefore the visually apparent structure is a statistical artifact, and the analyst should not attempt to model it directly. Instead one should utilize Box-Jenkins methodology, whereby appropriate significance levels for testing zero correlation can be obtained by fitting successively higher order MA models.