TESTING FOR ZERO AUTOCORRELATION WHEN THE INNOVATIONS BELONG TO THE NORMAL DOMAIN OF ATTRACTION OF A CAUCHY LAW

We consider the asymptotic null distribution of the empirical autocorrelation function when the innovations of a moving average process belong to the normal domain of attraction of a Cauchy law. A series expansion for the density of the limiting null distribution is developed, and some critical values of the tests are computed numerically.