The HPFARIMASPEC Procedure: INPUT Statement

The HPFARIMASPEC Procedure

INPUT options ;

The INPUT statements specify the transfer function inputs in the model. A separate INPUT statement is needed for each of the transfer function inputs. In this statement you can specify all the features of the transfer function associated with the input variable under consideration. The following options are used in the INPUT statement.

(SYMBOL|VAR)=variable

specifies a symbolic name for the dependent series. This symbol specification is optional. If the SYMBOL= option or the PREDEFINED= option is not specified, then X is used as a default symbol. If there are multiple INPUT statements, then an attempt is made to generate a unique set of input symbols.

PREDEFINED=option

associates a predefined trend or a set of seasonal dummy variables with this transfer function. The SYMBOL= and PREDEFINED= options are mutually exclusive.

In the following list of options, let $\text{[math]}$ represent the observation count from the start of the period of fit for the model, and let $\text{[math]}$ be the value of the time trend variable at observation $\text{[math]}$ .

LINEAR

a linear trend, with $\text{[math]}$

QUADRATIC

a quadratic trend, with $\text{[math]}$

CUBIC

a cubic trend, with $\text{[math]}$

INVERSE

an inverse trend, with $\text{[math]}$

SEASONAL

seasonal dummies. For a seasonal cycle of length $\text{[math]}$ , the seasonal dummy regressors include $\text{[math]}$ for models that include an intercept term, and $\text{[math]}$ for models that do not include an intercept term.

Each element of a seasonal dummy regressor is either zero or one, based on the following rule:

$\text{[math]}$

Note that if the model includes an intercept term, the number of seasonal dummy regressors is one less than $\text{[math]}$ to ensure that the linear system is full rank.

DIF=order

DIF=( order1, order2, ...)

specifies the differencing orders for the input series. See the DIF= option of the FORECAST statement for additional information.

DELAY=order

specifies the delay (or lag) order for the input series.

NUM=order

NUM= (lag, ..., lag ) ...(lag, ..., lag )

NUM= (lag, ..., lag )< $\text{[math]}$ > ...(lag, ..., lag )< $\text{[math]}$ >

specifies the numerator polynomial of the transfer function. See the P= option of the FORECAST statement for additional information about the polynomial order specification.

DEN=order

DEN= (lag, ..., lag ) ...(lag, ..., lag )

DEN= (lag, ..., lag )< $\text{[math]}$ > ...(lag, ..., lag )< $\text{[math]}$ >

specifies the denominator polynomial of the transfer function. See the P= option of the FORECAST statement for additional information about the polynomial order specification.

NC=value ...

lists starting values for the numerator polynomial coefficients.

DC=value ...

lists starting values for the denominator polynomial coefficients.

NZ=value

specifies the scale parameter—that is, the zero degree coefficient of the numerator.

TRANSFORM=option

specifies the transformation to be applied to the time series. The following transformations are provided:

NONE: no transformation applied
LOG: logarithmic transformation
SQRT: square-root transformation
LOGISTIC: logistic transformation
BOXCOX(n ): Box-Cox transformation with parameter number where number is between –5 and 5

When the TRANSFORM= option is specified, the intended time series must be strictly positive.

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