(a) Explain what stylised shapes would be expected for the autocorrelation and partial autocorrelation functions for the following stochastic processes:

• white noise

• an AR(2)

• an MA(1)

• an ARMA (2,1).

(b) Consider the following ARMA process.

Determine whether the MA part of the process is invertible.

(c) Produce one-, two-, three- and four-step-ahead forecasts for the process given in part

(b) of the question.

(d) Outline two criteria that are available for evaluating the forecasts produced in part

(c) of the question, highlighting the differing characteristics of each.

(e) What procedure might be used to estimate the parameters of an ARMA model? Explain, briefly, how such a procedure operates, and why OLS is not appropriate.