Abstract. We propose a new test to check the null hypothesis that the distribution of the inter-event times of a point process belongs to a parametric family of distributions. The test is based on the joint asymptotic normality of the total time on test and partial sum processes.

AMS Subject Classification (1991): 62N05, 62G10

Received August 23, 2004, and in revised form September 13, 2004. (Registered under 5878/2009.)