a. If forecasts are based on simple exponential smoothing, with xn t denoting the smoothed value of the series at time t, show that the error made in forecasting xt, standing at time 1t - 12, can be written as follows:

et = xt - xn t-1

b. Hence, show that we can write xn t = xt - 11 - a2et, from which we see that the most recent observation and the most recent forecast error are used to compute the next forecast.