The TIMESERIES Procedure

Seasonal Decomposition

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).