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

(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).

Univariate time series modelling and forecasting 263

(b) Consider the following ARMA process.
yt = 0.21 + 1.32yt−1 + 0.58ut−1 + ut Determine whether the MA part of the process is invertible.

(c) Produce 1-,2-,3- and 4-step-ahead forecasts for the process given in part (b).

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

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