1. The data file Earnings per Share shows earnings per share of a corporation over a period of 18 years. a. Using smoothing constants a = 0.8, 0.6, 0.4, and 0.2, find forecasts based on simple...

1. The data file Earnings per Share shows earnings per share of a corporation over a period of 18 years.

a. Using smoothing constants a = 0.8, 0.6, 0.4, and 0.2, find forecasts based on simple exponential smoothing.

b. Which of the forecasts would you choose to use?

2. a. If forecasts are based on simple exponential smoothing, with xnt 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:

b. Hence, show that we can write xnt = 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.