14.5 Monthly data for the Standard & Poor 500 Common Stock Price Index are shown in Table 14.1. The data are also plotted in Fig. 14.12.

(a) Using all but the last three data points (ie., April, May, and June of 1988). exponentially smooth the data using a value of .9 for the smoothing parameter

a. Hint: Remember that a moving average is always shorter than the original series. Repeat for a value of .2.

(b) Again using all but the last three data points, smooth the data using Holt's two- parameter exponential smoothing method. Set a 2 and y-.2. Explain how and why the results differ from those in

(a) above. Now use Eq. (14.36) to forecast the series out 1, 2. and 3 months. How close is your forecast to the actual values of the S&P 500 index for April to June 19887