1. Exponential smoothing
This is a widely used forecasting technique in retailing, even though it has not proven to be especially accurate.

2. Why is exponential smoothing so popular?
It's easy—the exotic term notwithstanding.
Data storage requirements are minimal (even though this is not the problem it once was due to plunging memory prices).
It is very cost effective when forecasts must be made for a large number of items--hence it has extensive use in retailing.

3. The basic algorithm (1) Where:
Lt is the forecast for the current period;
Xt is the most recent observation of the time series variable—such as, for example, sales last month of part #000897
Lt-1 is the most recent forecast; and
 is the smoothing constant, where 0 <  < 1

4. Equation (1) can be written as follows:
New Forecast = (New Data) + (1 - )Most Recent Forecast

5. Exponential smoothing is weighted moving average process
To demonstrate, let
(2)
Substitute (2) into (1):
(3)

6. But notice that:
Substitute (4) into (3) to obtain:
If we continue to substitute recursively, we get:

7. Notice that
are the weights attached to past values of X. Since  < 1, the weights attached to earlier or remoter observations of X are diminishing.

8. You don’t have to go through this recursive process each time you do a forecast. The process is summarized in the most recent forecast.

9. Selecting the smoothing constant ()
?alpha?
The range of possible values is zero and one.
If you select a value of  close to 1, that means you are attaching a large weight to the most recent observation. This is not indicated if your series is very choppy. For example, suppose you were forecasting the demand for part #56 in month t.
If you attached too much weight to the observation for t-1, you will have a large forecast error for month t.
Sales of part #56
t-2
t-1 t
Month

10. Application
We will now forecast sales of liquor and floor covering using this technique. We have monthly data for each variable beginning in January 1995 and running through July of 2000.

12. Summary statistics for monthly sales of floor covering and liquor sales, 1995:1 to 2000:7 (in millions of dollars)
Floor Covering
Liquor
Mean
Median
Maximum
Minimum
Std. Dev.
Observations 67

13. Liquor = 0.169 Floor covering = 0.127
The ratio of the standard deviation to the mean gives us a nice measure of the amplitude or volatility of a series month-to-month (or day-to-day, quarter-to-quarter, as the case may be).

14. Selecting the smoothing constant
Pricey time series forecasting software, such as EViews, use an algorithm to select the value of the smoothing constant that minimizes mean square error for in-sample forecasts.
If you lack this software, you can use a trial and error process.

15. The first set of estimates for monthly floor covering and liquor were produced by using the algorithm that selects the best performing value of the smoothing constant () for in-sample forecasts.
The second set of estimates is based on values of alpha () arbitrarily selected by the instructor.

16. Computer algorithm selects alpha to minimize MSE

17. Actual and smoothed values of floor covering, 1997:7 to 2000:7 (all data in millions of dollars)
Alpha = 0.706

18. Alpha selected arbitrarily

19. Sum of Squared Residuals
Statistics for the floor covering estimates
Alpha
Sum of Squared Residuals
Root Mean Square Error
0.30
94.67
0.7060
91.73
Data is for 1995:1 to 2000:7

20. Computer algorithm selects alpha to minimize MSE

21. Actual and smoothed values of liquor sales, 1997:7 to 2000:7 (all data in millions of dollars)
Alpha = 0.122

22. Alpha selected arbitrarily

23. Sum of Squared Residuals
Statistics for the liquor estimates
Alpha
Sum of Squared Residuals
Root Mean Square Error
0.45
343.1
0.122
312.4
Data is for 1995:1 to 2000:7

24. Forecasts for August, 2000 Remember our basic algorithm
Hence to forecast floor covering sales for August, 2000:
Floor CoveringAUG=(0.706)(1420) + [( )(1375)] = $
To forecast liquor sales
LiquorAUG=(0.122)(2560) + [( )(2349)] = $