1.5 (Forecasting with ARMA and SES) 10. You have estimated the following ARMA(1,1) model for some time series yt: yt = 0.036 + .69 ytl + 0.42 8151 + 3t Suppose that you have data for time to 1-1, i.e. you know that yt_1 = 3.4 and 33-1 = 1.3. a. Obtain forecasts for the series yr for times t, H], and t+2 using the estimated ARMA model. b. 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-ofsample) mean squared error. e. A colleague suggests that a simple exponential smoothing (SES) model might be more useful for forecasting the series. The estimated value of the smoothing constant, (I, is 0.15, with the most recently available smoothed value, Sm = 0.0305. Obtain forecasts for the series y: for times 1', 15+ 1, and t+2 using this model. (1. Given your answers to parts (a) to (c) of the question, determine whether ARMA or exponential smoothing models give the most accurate forecasts in this application. Please use programming R to solve the question, Thank you very much