Exercises. 1. The following time series shows the sales of a particular product over the past 12 month.

1. The following time series shows the sales of a particular product over the past 12 month.

Month	Sales	Month	Sales

Use to compute the simple exponential smoothing to obtain forecasts of sales over the next three months. Graph the observed time series and the forecasts.

2. The following table gives the gross domestic product (in billions of dollars) of the country for the years 1990 through 1997.

Year	GDP
	1768.4 1974.1 2488.6 3030.6 3405.0 4038.7 4268.6 4900.4

Use the method of simple exponential smoothing, with a smoothing constant of , to obtain forecasts of GDP for the next two years. Graph the observed time series and the forecasts.

3. The following table shows the year-end price of gold (in dollars) over 10 consecutive years.

Year	Price ($)

Use the method of simple exponential smoothing, with a smoothing constant of , to obtain forecasts of the price of gold in the next four years. Graph the observed time series and the forecasts.

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