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), pseudoadditive (MODE=PSEUDOADD), and logadditive (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 HodrickPrescott filter parameter (Hodrick and Prescott, 1980). The default is LAMBDA=1600. The HodrickPrescott filter is used to decompose the trendcycle 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 


trendcycle component 
TCC 
MULT 
centered moving average of 
ADD 
centered moving average of 

LOGADD 
centered moving average of 

PSEUDOADD 
centered moving average of 

seasonalirregular 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 


trendcycleseasonal 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 trendcycle component is computed from the period centered moving average as follows:
When is even the trendcycle component is computed from the period centered moving average as follows:
The seasonal component is obtained by averaging the seasonalirregular component for each season.
where and . The seasonal components are normalized to sum to one (multiplicative) or zero (additive).