transforms the input series, , by using a BoxCox power transformation,
The power must be specified (for example, POWER=0.33). The default is no transformation (); that is, POWER=1. The log transformation (POWER=0), square root transformation (POWER=0.5), and the inverse transformation
(POWER=–1) are equivalent to the corresponding FUNCTION= option.
Table 37.6: Power Values Related to the Census Bureau Function Argument
FUNCTION=

Transformation

Range for

Equivalent Power Argument

NONE


All values

POWER=1

LOG


for all t

POWER=0

SQRT


for all t

POWER=0.5

INVERSE


for all t

POWER=–1

LOGISTIC


for all t

No equivalent

specifies the transformation to be applied to the series prior to estimating a regARIMA model. The transformation used by
FUNCTION=NONE, LOG, SQRT, INVERSE, or LOGISTIC is related to the POWER= option as shown in Table 37.6. FUNCTION=AUTO uses selection based on Akaike’s information criterion (AIC) to decide between a log transformation and no
transformation. The default is FUNCTION=NONE.
However, the FUNCTION= and POWER= options are not completely equivalent. In some cases, using the FUNCTION= option causes
the program to automatically select other options. For example, FUNCTION=NONE causes the default mode to be MODE=ADD in the
X11 statement. Also, the choice of transformation invoked by the FUNCTION=AUTO option can impact the default mode of the X11
statement.
There are restrictions on the value used in the POWER= and FUNCTION= options when preadjustment factors for seasonal adjustment
are generated from a regARIMA model. When seasonal adjustment is requested with the X11 statement, any value of the POWER
option can be used for the purpose of forecasting the series with a regARIMA model. However, this is not the case when factors
generated from the regression coefficients are used to adjust either the original series or the final seasonally adjusted
series. In this case, the only accepted transformations are the log transformation, which can be specified as POWER=0 for
multiplicative or logadditive seasonal adjustments, and no transformation, which can be specified as POWER=1 for additive
seasonal adjustments. If no seasonal adjustment is performed, any POWER transformation can be used. The preceding restrictions
also apply when FUNCTION=NONE and FUNCTION=LOG are specified.