ANSWER ALL PARTS

(b) Consider modelling the time series Y4 representing the yearly GDP of Mauritius for the last 50 years. (i) The table below lists part of the acf of Y4 and the acf and pacf of the first difference of Yt. 2 3 4 5 6 7 8 9 10 0.76 0.71 0.67 0.55 0.49 0.44 0.41 0.39 0.32 Lag 1 acf Yt 0.85 acf vYt 0.377 pacf vY 0.377 -0.056 0.003 0.089 -0.012 -0.076 0.077 0.134 -0.191 0.102 -0.126 -0.0120.111 0.004 -0.036 0.074 | 0.053 0.139 0.010 (i) Explain the reason for taking first differences. [2 marks] (ii) Explain why the first ACF and PACF values are similar. [2 marks] (iii) Discuss, showing any calculations you make, potential ARIMA mod- els that would fit the data. [4 marks) (iv) After fitting a suitable model to the above data in R, describe briefly how you would check the adequacy of the fitted model using the estimated residuals. (5 marks]