Consider an ARMA(11) process with AR parameter MA parameter and variance v.

(a) Simulate 400 observations from a process with = 09 = 06 and v =1

(b) Compute the conditional least squares estimates of and based on the 400 observations simulated above.

(c) Implement a MCMC algorithm to obtain samples from the posterior distribution of , and v under the conditional likelihood. Assume a uniform prior distribution in the stationary and invertibility regions for and and a prior of the form (v) 1 v on the variance parameter. Summarize your posterior inference and forecasting (for up to 100 steps ahead) under this model.