EXAMPLE 20.2.1 Here is a lognormal model. Let the processes {Ut } and { Vt } be independent of each other, {Ut } is Gaussian white noise, and ln Vt ∼ N

(a, b2). One simple way to achieve this as well as to make both { |Xt −μ| }’s and { (Xt −μ)2 }’s autocorrelations positive is to posit the following AR(1) model for { ln Vt }:
ln(Vt )−α = θ(ln(Vt−1)−α)+ξt, θ>0.