Suppose Z, is white noise with mean zero. After suitable pre-processing, the monthly sales of a consumer product was modelled by the process X1 = 0.242X,-1 + Z, + 0.27121-1. Five years of monthly observations were used in fitting the above model, the most recent observation being -9.171 and the corresponding fitted value being -4.163. The estimate of the standard deviation of Z, is found to be 5.573. Provide answers to the following to three decimal places. Part (a) Using the model, provide a prediction for the next value in the series