An exponential moving-average sequence and point process (EMA1)

A construction is given for a stationary sequence of random variables {X,} which have exponential marginal distributions and are random linear combinations of order one of an i.i.d. exponential sequence {, }. The joint and trivariate exponential distributions of X,_-, X, and X,,, are studied, as weJl as the intensity function, point spectrum and variance time curve for the point process which has the {X,} sequence for successive times between events. Initial conditions to make the point process count stationary are given, and extensions to higherorder moving averages and Gamma point processes are discussed. POINT PROCESS; EXPONENTIAL INTERVALS; CORRELATED EXPONENTIAL SEQUENCE; MOVING AVERAGE STRUCTURE; SPECTRUM OF COUNTS; BIVARIATE EXPONENTIAL DISTRIBUTION; CONDITIONAL CORRELATION; STATIONARY INITIAL CONDITIONS