Question 7 The following plots have been obtained for a time series. a) Suggest an appropriate ARIMA model. (2 marks). 120 90- 60 30 - 1980 Jan 1980 Jan 2000 Jan 2010 Jan 2020 Jan Month 0.2- 0.2 pact TTTT -0.1- -0.1 - 12 18 24 12 10 24 lag [1M] lag [1M] b) The following ARIMA output has been obtained from R. Based on this output, which model would you recommend for forecasting? (2 marks). . model sigma2 log_lik AIC AICC BIC ar_roots ma_roots ## 1 arima0ll 17 .1 -1380. 2788. 2780. 2813. ## 2 arimallo 17.1 -1389. 2790. 2790. 2815. ## 3 auto 17.4 -1392. 2798. 2798. 2827. c) If your selected model in part b) above has a p-value of 0.13 in the Ljung-Box test, would you recommend using this model? Explain why or why not. (2 marks)