The following problems are based on the material in Section 3.9. (a) For the DAR(1) model in (3.41), show that the support of X t and Z t are the same, and then derive the ACF. (b) Show that the...

The following problems are based on the material in Section 3.9.

(a) For the DAR(1) model in (3.41), show that the support of X_t
and Z_t
are the same, and then derive the ACF.

(b) Show that the marginal distribution of X_t
defined by (3.42) is Geometric with parameter p, and then show the ACF is that of an AR(1) model.

(c) Show that the marginal of X_t
in (3.43) is Poisson if Z_t
is Poisson, and then derive the ACF of X_t