This question concerns a time series model for continuous and positive outcomes yt. Suppose a series xt follows a stationary AR(1) model with parameters v and the usual normal innovations. De ne a transformed time series yt = exp( +xt) for each t for some known constant

(a) Show that yt a rst-order Markov process.

(b) Is yt a stationary process?

(c) Find E(ytyt 1) as a function of yt 1 and show that it has the form E(ytyt 1) = ayt 1 for some positive constant aGive an expression for a in terms of v

(d) Can you imagine applied time series contexts that might utilize this simple model as a component? Comment on potential uses.