10. You have estimated the following ARMA(1,1) model for some time-series data y; = 0.036 + 0.6%.; + 0.421;\

10. You have estimated the following ARMA(I,I) model for some time-series data yt = 0.036 + 0.69yt-l + 0.42ut-1 + Suppose that you have data for time to t 1, i.e., you know that yt (a) (b) (c) (d) 3.4, and = 1.3 Obtain forecasts for the series y for times t, t + 1, and t + 2 using the estimated ARMA model. If the actual values for the series turned out to be 0.032, 0.961, 0.203 for t, t + 1, t + 2, calculate the (out-of-sample) mean squared error. A colleague suggests that a simple exponential smoothing model might be more useful for forecasting the series. The estimated value of the smoothing constant is 0.15, with the most recently available smoothed value, St-l being 0.0305. Obtain forecasts for the series y for times t, t +1, and t +2 using this model. Given your answers to parts (a) to (c) of the question, determine whether BoxJenkins or exponential smoothing models give the most accurate forecasts in this application.