
BACKCAST= n

specifies the number of years to backcast the series. The default is BACKCAST= 0. See the section Effect of Backcast and Forecast Length for details.

CHICR= value

specifies the criteria for the significance level for the BoxLjung chisquare test for lack of fit when testing the five
predefined models. The default is CHICR= 0.05. The CHICR= option values must be between 0.01 and 0.90. The hypothesis being
tested is that of model adequacy. Nonrejection of the hypothesis is evidence for an adequate model. Making the CHICR= value
smaller makes it easier to accept the model. See the section Criteria Details for further details on the CHICR= option.

CONVERGE= value

specifies the convergence criterion for the estimation of an ARIMA model. The default value is 0.001. The CONVERGE= value
must be positive.

FORECAST= n

specifies the number of years to forecast the series. The default is FORECAST= 1. See the section Effect of Backcast and Forecast Length for details.

MAPECR= value

specifies the criteria for the mean absolute percent error (MAPE) when testing the five predefined models. A small MAPE value
is evidence for an adequate model; a large MAPE value results in the model being rejected. The MAPECR= value is the boundary
for acceptance/rejection. Thus a larger MAPECR= value would make it easier for a model to pass the criteria. The default is
MAPECR= 15. The MAPECR= option values must be between 1 and 100. See the section Criteria Details for further details on the MAPECR= option.

MAXITER= n

specifies the maximum number of iterations in the estimation process. MAXITER must be between 1 and 60; the default value
is 15.

METHOD= CLS


METHOD= ULS
METHOD= ML

specifies the estimation method. ML requests maximum likelihood, ULS requests unconditional least squares, and CLS requests
conditional least squares. METHOD=CLS is the default. The maximum likelihood estimates are more expensive to compute than
the conditional least squares estimates. In some cases, however, they can be preferable. For further information on the estimation
methods, see Estimation Details in Chapter 7: The ARIMA Procedure.

MODEL= ( P=n1 Q=n2 SP=n3 SQ=n4 DIF=n5 SDIF=n6 <NOINT> <CENTER>)

specifies the ARIMA model. The AR and MA orders are given by P=n1 and Q=n2, respectively, while the seasonal AR and MA orders are given by SP=n3 and SQ=n4, respectively. The lag corresponding to seasonality is determined by the MONTHLY or QUARTERLY statement. Similarly, differencing
and seasonal differencing are given by DIF=n5 and SDIF=n6, respectively.
For example
arima model=( p=2 q=1 sp=1 dif=1 sdif=1 );
specifies a (2,1,1)(1,1,0)s model, where s, the seasonality, is either 12 (monthly) or 4 (quarterly). More examples of the MODEL= syntax are given in the section Details of Model Selection.

NOINT

suppresses the fitting of a constant (or intercept) parameter in the model. (That is, the parameter is omitted.)

CENTER

centers each time series by subtracting its sample mean. The analysis is done on the centered data. Later, when forecasts
are generated, the mean is added back. Note that centering is done after differencing. The CENTER option is normally used
in conjunction with the NOCONSTANT option of the ESTIMATE statement.
For example, to fit an AR(1) model on the centered data without an intercept, use the following ARIMA statement:
arima model=( p=1 center noint );

NOPRINT

suppresses the normal printout generated by the ARIMA statement. Note that the effect of specifying the NOPRINT option in
the ARIMA statement is different from the effect of specifying the NOPRINT in the PROC X11 statement, since the former only
affects ARIMA output.

OVDIFCR= value

specifies the criteria for the overdifferencing test when testing the five predefined models. When the MA parameters in one
of these models sum to a number close to 1.0, this is an indication of overparameterization and the model is rejected. The
OVDIFCR= value is the boundary for this rejection; values greater than this value fail the overdifferencing test. A larger
OVDIFCR= value would make it easier for a model to pass the criteria. The default is OVDIFCR= 0.90. The OVDIFCR= option values
must be between 0.80 and 0.99. See the section Criteria Details for further details on the OVDIFCR= option.

PRINTALL

provides the same output as the default printing for all models fit and, in addition, prints an estimation summary and chisquare
statistics for each model fit. See Printed Output for details.

PRINTFP

prints the results for the initial pass of X11 made to exclude tradingday effects. This option has an effect only when the
TDREGR= option specifies ADJUST, TEST, or PRINT. In these cases, an initial pass of the standard X11 method is required to
get rid of calendar effects before doing any ARIMA estimation. Usually this first pass is not of interest, and by default
no tables are printed. However, specifying PRINTFP in the ARIMA statement causes any tables printed in the final pass to also
be printed for this initial pass.

TRANSFORM= (LOG)  LOG


TRANSFORM= ( constant ** power )

The ARIMA statement in PROC X11 allows certain transformations on the series before estimation. The specified transformation
is applied only to a userspecified model. If TRANSFORM= is specified and the MODEL= option is not specified, the transformation
request is ignored and a warning is printed.
The LOG transformation requests that the natural log of the series be used for estimation. The resulting forecast values are
transformed back to the original scale.
A general power transformation of the form is obtained by specifying
transform= ( a ** b )
If the constant a is not specified, it is assumed to be zero. The specified ARIMA model is then estimated using the transformed series. The
resulting forecast values are transformed back to the original scale.