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 following option 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 Census Bureau function argument.

Table 5.2: 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

Note that there are restrictions on the value used in the POWER option 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.

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