1.

(a) Use the derivations in Section 8.2 and Chapter 6, Section 6.4 to obtain a posterior simulator for the local level model with independent Student-t errors. You may use whatever prior you wish for the model parameters

(although the natural conjugate one of Section 6.4 will be the easiest).

(b) Write a program which uses your result from part

(a) and test the program on either real data (e.g. the industrial production data from the empirical illustration in Section 8.3.2) or artificial data generated according to various data generating processes.

(c) Add to your program code for calculating the marginal likelihood for the local level model with independent Student-t errors. For your data set(s)

calculate the Bayes factor comparing the local level model with Normal errors to the local level model with Student-t errors.