Let xt be a stationary normal process with mean x and autocovariance function (h). Define the nonlinear time series yt = exp{xt}. (a) Express the

Let xt be a stationary normal process with mean µx and autocovariance function γ(h). Define the nonlinear time series yt = exp{xt}.

(a) Express the mean function E(yt) in terms of µx and γ(0). The moment generating function of a normal random variable x with mean µ and variance σ2 is Mx(λ) = E[exp{λx}] = exp

µλ +

1 2

σ2λ2



.

(b) Determine the autocovariance function of yt. The sum of the two normal random variables xt+h + xt is still a normal random variable.