Simulate an IMA(1,1) process with = 0.8 and 0 = 0. Simulate 35 values, but set aside the last five values to compare forecasts with actual values. (a) Using the first 30 values of the series, find the value for the maximum likelihood estimate of . (b) Using the estimated model, forecast the next five values of the series. Plot the series together with the five forecasts. What is special about the forecasts? (c) Compare the five forecasts with the actual values that you set aside. (d) Plot the forecasts together with 95% forecast limits. Do the actual values fall within the forecast limits? (e) Repeat parts (a) through (d) with a new simulated series using the same values of the parameters and same sample size