Suppose that a (0, 1, 1) model ∇???????? = (1 − ????????)????????, corresponding to the use of an exponentially weighted moving average forecast, with ???? arbitrarily chosen to be equal to 0.5, was used to forecast a series that was, in fact, well represented by the

(0, 1, 2) model ∇???????? = (1 − 0.9???? + 0.2????2)????????.

(a) Calculate the autocorrelation function of the lead 1 forecast errors ???????? obtained from the (0, 1, 1) model.

(b) Show how this ACF could be used to identify a model for the ???????? series, leading to the identification of a (0, 1, 2) model for the ???????? series.