ABSTRACT
The implications of the process et on the correlation structure in the Yt 's and the regression model is as follows. Note first that e; = exp(et) has a log-normal distribution with mean a = exp( ~0'2 ) and variance v2 = exp(2£T2) - exp( £T2). It follows upon integration over et, that the marginal mean of Yt is given by
exp((x~m))' f3(m)) E( exp( et)) a exp((x~m))'f3(m)),
and
so that
(4)
(5)
From ( 4) and ( 5), we see that the unobserved process ft allows for overdispersion and autocorrelation into Yt· In addition, the degree of overdispersion depends on fJt. The autocorrelation in Yt must be less than or equal to that in ft and the degree of autocorrelation in Yt relative to ft decreases as !Jt and v 2 decrease.
