Seasonal decomposition/analysis can be performed on the working series by specifying the OUTDECOMP= option, the PRINT=DECOMP option, or one of the PLOTS= options associated with decomposition in the PROC TIMESERIES statement. The DECOMP statement enables you to specify options related to decomposition. The TIMESERIES procedure uses classical decomposition. More complex seasonal decomposition/adjustment analysis can be performed by using the X11 or the X12 procedure of SAS/ETS.
The DECOMP statement MODE= option determines the mode of the seasonal adjustment decomposition to be performed. There are four modes: multiplicative (MODE=MULT), additive (MODE=ADD), pseudo-additive (MODE=PSEUDOADD), and log-additive (MODE=LOGADD) decomposition. The default is MODE=MULTORADD which specifies MODE=MULT for series that are strictly positive, MODE=PSEUDOADD for series that are nonnegative, and MODE=ADD for series that are not nonnegative.
When MODE=LOGADD is specified, the components are exponentiated to the original metric.
The DECOMP statement LAMBDA= option specifies the Hodrick-Prescott filter parameter (Hodrick and Prescott, 1980). The default is LAMBDA=1600. The Hodrick-Prescott filter is used to decompose the trend-cycle component into the trend component and cycle component in an additive fashion. A smaller parameter assigns less significance to the cycle; that is, LAMBDA=0 implies no cycle component.
The notation and keywords associated with seasonal decomposition/adjustment analysis are defined in Table 32.3.
Table 32.3: Seasonal Adjustment Formulas
Component |
Keyword |
MODE= Option |
Formula |
---|---|---|---|
original series |
ORIGINAL |
MULT |
|
ADD |
|
||
LOGADD |
|
||
PSEUDOADD |
|
||
trend-cycle component |
TCC |
MULT |
centered moving average of |
ADD |
centered moving average of |
||
LOGADD |
centered moving average of |
||
PSEUDOADD |
centered moving average of |
||
seasonal-irregular component |
SIC |
MULT |
|
ADD |
|
||
LOGADD |
|
||
PSEUDOADD |
|
||
seasonal component |
SC |
MULT |
seasonal Averages of |
ADD |
seasonal Averages of |
||
LOGADD |
seasonal Averages of |
||
PSEUDOADD |
seasonal Averages of |
||
irregular component |
IC |
MULT |
|
ADD |
|
||
LOGADD |
|
||
PSEUDOADD |
|
||
trend-cycle-seasonal component |
TCS |
MULT |
|
ADD |
|
||
LOGADD |
|
||
PSEUDOADD |
|
||
trend component |
TC |
MULT |
|
ADD |
|
||
LOGADD |
|
||
PSEUDOADD |
|
||
cycle component |
CC |
MULT |
|
ADD |
|
||
LOGADD |
|
||
PSEUDOADD |
|
||
seasonally adjusted series |
SA |
MULT |
|
ADD |
|
||
LOGADD |
|
||
PSEUDOADD |
|
When is odd the trend-cycle component is computed from the -period centered moving average as follows:
When is even the trend-cycle component is computed from the -period centered moving average as follows:
The seasonal component is obtained by averaging the seasonal-irregular component for each season.
where and . The seasonal components are normalized to sum to one (multiplicative) or zero (additive).