The following plots have been obtained for a time series. a) Suggest an appropriate ARIMA model. (2 marks). 250 200 150 100 50 0 2000 Jan 02- 0.1- 0.0 0.1- 2005 Jan) 2010 Jan pac 02- 0.1 0.3 -0.1 2015 Jan nowing 2020 Jan mphoed lug [1M) ag [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 ## ## 1 arima011 ## 2 arima110 ## 3 auto sigma2 log_lik AIC AICC BIC ar roots 17.1 -1393. 2778. 2778. 2806. 17.1 -1399. 2780. 2780. 2815. 17.4 -1392. 2788. 2788. 2807. ma_roots c) If your selected model in part b) above has a p-value of 0.009 in the Ljung-Box test, would you recommend using this model? Explain why or why not. (2 marks).