TRANSFORM Statement

The X12 Procedure

TRANSFORM Statement

TRANSFORM options;

The TRANSFORM statement transforms or adjusts the series prior to estimating a regARIMA model. With this statement, the series can be Box-Cox (power) transformed. The Prior Adjustment Factors table is associated with the TRANSFORM statement.

Only one of the following options can appear in the TRANSFORM statement.

POWER= value

Transform the input series Y_t using a Box-Cox power transformation,

${Y_t arrow y_t}=\{ {log(Y_t)} & {\lambda=0}\ {\lambda^2 + (Y_t^\lambda - 1)/\lambda} & {\lambda \neq 0} .$

The power $\lambda$ must be specified (for example, POWER= .33). The default is no transformation ( $\lambda=1$ ); that is, POWER= 1. The log transformation (POWER= 0), square root transformation (POWER= .5), and the inverse transformation (POWER= -1) are equivalent to the corresponding FUNCTION= option.

Table 6.2: Power Values Related to the Census Bureau Function Argument

function=	transformation	range for Y_t	equivalent power argument
none	Y_t	all values	power = 1
log	log(Y_t)	Y_t > 0 for all t	power = 0
sqrt	$2(\sqrt{Y_t} - 0.875)$	$Y_t \geq 0$ for all t	power = 0.5
inverse	2 - [1/(Y_t)]	$Y_t \neq 0$ for all t	power = -1
logistic	log([(Y_t)/(1 - Y_t)])	0 < Y_t < 1 for all t	none equivalent

FUNCTION=NONE

FUNCTION=LOG

FUNCTION=SQRT

FUNCTION=INVERSE

FUNCTION=LOGISTIC

FUNCTION=AUTO

The transformation used by FUNCTION=NONE, LOG, SQRT, INVERSE, and LOGISTIC is related to the POWER= option as shown in Table 6.2. FUNCTION=AUTO uses an AIC-based selection 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 instance, 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 may impact the default mode of the X11 statement.

Note that 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 log-additive 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 to FUNCTION=NONE and FUNCTION=LOG.

Chapter Contents
Previous
Next
Top