3. Consider the ARMA(3, 2) process Yt = -0.5Y+-1 + 0.34Yt -2 + 0.08Yt-3 + Zt - 0.2Zt-1 - 0.08Zt-2, where {Zt} is a white noise process with unit variance. It is known that the above process is overestimated. (a) Suggest a parsimonious model for the above process. [3 marks] (b) Find the first three lags of the autocorrelation function (ACF) for the process. You may use the fact that the process is stationary and invertible. [12 marks] (c) If Y521 = 1, Y520 = 0.8, Y519 = -0.5 and Z521 = 0.3, find the 1-step, 2-step and 3-step ahead forecasts for the time series at t = 521. [5 marks] (d) If Y524 = -0.4, find the forecast error of the 3-step ahead forecast in (c), and find the standard deviation of the forecast error. [5 marks]