The SMOOTH function computes a single or a double exponential smoothing of a numeric expression.
DECIMAL
SMOOTH(expression {SINGLE alpha|DOUBLE alpha beta m} [BASEDON dimension-list])
The numeric expression whose values are to be smoothed.
The method to use in the exponential smoothing of the values in expression. The SINGLE method specifies single exponential smoothing and requires an alpha argument. The DOUBLE method specifies double exponential smoothing (also known as Holt's linear exponential smoothing) and requires an alpha argument, a beta argument, and an m argument.
A number in the range from 0 to 1 that smooths the difference between the observed data forecast and the last forecast. The higher the value, the more weight the most recent forecast has, so smoothing decreases as the smoothing factor increases. A smoothing factor of 0 completely smooths the forecasts and always returns the first forecast, which is the first data observation. A smoothing factor of 1 produces no smoothing at all and returns the previous data observation. (See "Results of alpha Values".)
A number in the range from 0 to 1 that smooths the difference between the previous forecast and the current forecast. As with the alpha argument, smoothing decreases as the smoothing factor increases.
A positive INTEGER
between 1 and the total number of periods of data in the data series. The m argument specifies the number of periods on which to base the forecasts.
An optional list of one or more of the dimensions of expression to include in the exponential smoothing. When you do not specify the dimensions, then SMOOTH bases the smoothing on all of the dimensions of expression.
The Effect of NASKIP on SMOOTH
SMOOTH is affected by the NASKIP option. When NASKIP is set to YES
(the default), then SMOOTH ignores NA
values. When NASKIP is set to NO
, then SMOOTH returns NA
for every forecast after the NA
value.
This note illustrates the results of using different alpha values for single exponential smoothing. The results are based on the sales
variable with the dimensions limited by the following statements.
LIMIT month TO 'Jan96' TO 'Dec96' LIMIT product TO 'Tents' LIMIT district TO 'Boston' REPORT DOWN month SMOOTH(sales, SINGLE, ALPHA, BASEDON month)
The following table shows the data values of the sales
variable and also shows the results of the SMOOTH function in the preceding statement when the alpha argument variable has the different values shown in the table.
MONTH | Sales of tents in Boston | alpha = 0 | alpha = .1 | alpha = .5 | alpha = .9 |
---|---|---|---|---|---|
Jan96 | 50,808.96 | NA | NA | NA | NA |
Feb96 | 34,641.59 | 50,808.96 | 50,808.96 | 50,808.96 | 50,808.96 |
Mar96 | 45,742.21 | 50,808.96 | 49,192.22 | 42,725.28 | 36,258.33 |
Apr96 | 61,436.19 | 50,808.96 | 48,847.22 | 44,233.74 | 44,793.82 |
May96 | 86,699.67 | 50,808.96 | 50,106.12 | 52,834.97 | 59,771.95 |
Jun96 | 95,120.83 | 50,808.96 | 53,765.47 | 69,767.32 | 84,006.90 |
Jul96 | 93,972.49 | 50,808.96 | 57,901.01 | 82,444.07 | 94,009.44 |
Aug96 | 94,738.05 | 50,808.96 | 61,508.16 | 88,208.28 | 93,976.18 |
Sep96 | 75,407.66 | 50,808.96 | 64,831.15 | 91,473.17 | 94,661.86 |
Oct96 | 70,622.91 | 50,808.96 | 65,888.80 | 83,440.41 | 77,333.08 |
Nov96 | 46,124.99 | 50,808.96 | 66,362.21 | 77,031.66 | 71,293.93 |
Dec96 | 36,938.27 | 50,808.96 | 64,338.49 | 61,578.33 | 48,641.88 |
Example 8-100 Smoothing Values
These statements limit the dimensions of the sales
variable, set the data column width for reports, and report the data values for sales
.
LIMIT month TO 'Jan96' TO 'Dec96' LIMIT product TO 'Tents' LIMIT district TO 'Boston' COLWIDTH = 14 REPORT W 6 DOWN month sales
The preceding statements produce the following output.
DISTRICT: Boston ----SALES----- ---PRODUCT---- MONTH Tents ------ -------------- Jan96 50,808.96 Feb96 34,641.59 Mar96 45,742.21 Apr96 61,436.19 ... Nov96 46,124.99 Dec96 36,938.27
This statement reports the results of using the SMOOTH function on the sales
variable with the SINGLE method, a data smoothing factor of .5
, and based on the month
dimension.
REPORT W 6 DOWN month SMOOTH(sales, SINGLE, .5, BASEDON month)
The preceding statement produces the following output.
DISTRICT: Boston SMOOTH(SALES,- -SINGLE, .5,-- BASEDON MONTH) ---PRODUCT---- MONTH Tents ------ -------------- Jan96 NA Feb96 50,808.96 Mar96 42,725.28 Apr96 44,233.74 ... Nov96 77,031.66 Dec96 61,578.33