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The ARIMA Procedure |

**ESTIMATE***options;*

Options used in the ESTIMATE statement are described in the following sections.

**ALTPARM**-
specifies the alternative parameterization of the overall scale of
transfer functions in the model.
See the section "Alternative Model Parameterization" later in this chapter for details.
**INPUT=***variable***INPUT= (***transfer-function variable*... )-
specifies input variables and their transfer functions.

The variables used on the INPUT= option must be included in the CROSSCORR= list in the previous IDENTIFY statement. If any differencing is specified in the CROSSCORR= list, then the differenced series is used as the input to the transfer function.

The transfer function specification for an input variable is optional. If no transfer function is specified, the input variable enters the model as a simple regressor. If specified, the transfer function specification has the following syntax:

*S*$ (*L*,_{1,1}*L*, ... ) (_{1,2}*L*, ... ) ... / (_{2,1}*L*_{j,1}, ... ) ...

Here,*S*is a shift or lag of the input variable, the terms before the slash (/) are numerator factors, and the terms after the slash (/) are denominator factors of the transfer function. All three parts are optional. See the section "Specifying Inputs and Transfer Functions" later in this chapter for details. **METHOD=ML****METHOD=ULS****METHOD=CLS**-
specifies the estimation method to use.
METHOD=ML specifies the maximum likelihood method.
METHOD=ULS specifies the unconditional least-squares method.
METHOD=CLS specifies the conditional least-squares method.
METHOD=CLS is the default.
See the section "Estimation Details" later in this chapter for more information.
**NOCONSTANT****NOINT**-
suppresses the fitting of a constant (or intercept) parameter in the model.
(That is, the parameter is omitted.)
**NODF**-
estimates the variance by dividing the error sum of
squares (SSE) by the number of residuals.
The default is to divide the SSE by the number of residuals minus
the number of free parameters in the model.
**NOPRINT**-
suppresses the normal printout generated by the ESTIMATE statement.
If the NOPRINT option is specified for the ESTIMATE statement, then any
error and warning messages are printed to the SAS log.
**P=***order***P= (***lag, ..., lag*) ... (*lag, ..., lag*)-
specifies the autoregressive part of the model.
By default, no autoregressive parameters are fit.

P=(*l*_{1},*l*_{2}, ...,*l*_{k}) defines a model with autoregressive parameters at the specified lags. P=*order*is equivalent to P=(1, 2, ...,*order*).

A concatenation of parenthesized lists specifies a factored model. For example, P=(1,2,5)(6,12) specifies the autoregressive model

**PLOT**-
plots the residual autocorrelation functions.
The sample autocorrelation, the sample inverse autocorrelation,
and the sample partial autocorrelation functions of the model residuals
are plotted.
**Q=***order***Q= (***lag, ..., lag*) ... (*lag, ..., lag*)-
specifies the moving-average part of the model.
By default, no moving-average part is included in the model.

Q=(*l*_{1},*l*_{2}, ...,*l*_{k}) defines a model with moving-average parameters at the specified lags. Q=*order*is equivalent to Q=(1, 2, ...,*order*). A concatenation of parenthesized lists specifies a factored model. The interpretation of factors and lags is the same as for the P= option.

**OUTEST=***SAS-data-set*-
writes the parameter estimates to an output data set.
If the OUTCORR or OUTCOV option is used, the correlations or
covariances of the estimates are also written to the OUTEST= data set.
See the section "OUTEST= Data Set" later in this chapter
for a description of
the OUTEST= output data set.
**OUTCORR**-
writes the correlations of the parameter estimates to the OUTEST= data set.
**OUTCOV**-
writes the covariances of the parameter estimates to the OUTEST= data set.
**OUTMODEL=***SAS-data-set*-
writes the model and parameter estimates to an output data set.
If OUTMODEL= is not specified, no model output data set is created.
See the section "OUTMODEL= Data Set" for a description of
the OUTMODEL= output data set.
**OUTSTAT=***SAS-data-set*-
writes the model diagnostic statistics to an output data set.
If OUTSTAT= is not specified, no statistics output data set is created.
See the section "OUTSTAT= Data Set" later in this chapter for a
description of
the OUTSTAT= output data set.

If values for any parameters are specified, values for all parameters should be given. The number of values given must agree with the model specifications.

**AR=***value*...-
lists starting values for the autoregressive parameters.
See "Initial Values" later in this chapter for more information.
**INITVAL= (***initializer-spec variable*... )-
specifies starting values for the parameters in the transfer
function parts of the model.
See "Initial Values" later in this chapter for more information.
**MA=***value*...-
lists starting values for the moving-average parameters.
See "Initial Values" later in this chapter for more information.
**MU=***value*-
specifies the MU parameter.
**NOEST**-
uses the values specified with the AR=, MA=, INITVAL=, and MU= options as
final parameter values.
The estimation process is suppressed except for estimation of the residual variance.
The specified parameter values are used directly by the next FORECAST statement.
When NOEST is specified, standard errors,
*t*values, and the correlations between estimates are displayed as 0 or missing. (The NOEST option is useful, for example, when you wish to generate forecasts corresponding to a published model.)

**BACKLIM= -***n*-
omits the specified number of initial residuals from the sum of squares or
likelihood function.
Omitting values can be useful for suppressing transients in
transfer function models that are sensitive to start-up values.
**CONVERGE=***value*-
specifies the convergence criterion.
Convergence is assumed when the largest change in the estimate for
any parameter is less that the CONVERGE= option value.
If the absolute value of the parameter estimate is greater than 0.01,
the relative change is used; otherwise, the absolute change in the
estimate is used.
The default is CONVERGE=.001.
**DELTA=***value*-
specifies the perturbation value for computing numerical derivatives.
The default is DELTA=.001.
**GRID**-
prints the error sum of squares (SSE) or concentrated log likelihood
surface in a small grid of the parameter space around the final estimates.
For each pair of parameters, the SSE is printed for the
nine parameter-value combinations formed by the grid,
with a center at the final estimates and with spacing given by
the GRIDVAL= specification.
The GRID option may help you judge whether the estimates are truly
at the optimum, since the estimation process does not always converge.
For models with a large number of parameters,
the GRID option produces voluminous output.
**GRIDVAL=***number*-
controls the spacing in the grid printed by the GRID option.
The default is GRIDVAL=0.005.
**MAXITER=***n***MAXIT=***n*-
specifies the maximum number of iterations allowed.
The default is MAXITER=50.
(The default was 15 in previous releases of SAS/ETS software.)
**NOLS**-
begins the maximum likelihood or unconditional least-squares
iterations from the preliminary estimates rather than from the
conditional least-squares estimates that are produced after four
iterations.
See the section "Estimation Details" later in this chapter for details.
**NOSTABLE**-
specifies that the autoregressive and moving-average parameter estimates
for the noise part of the model not be restricted to the
stationary and invertible regions, respectively.
See the section "Stationarity and Invertibility" later in this chapter for more information.
**PRINTALL**-
prints preliminary estimation results and the iterations in the final
estimation process.
**SINGULAR=***value*-
specifies the criterion for checking singularity.
If a pivot of a sweep operation is less than the SINGULAR= value,
the matrix is deemed singular. Sweep operations are performed
on the Jacobian matrix during final estimation and on the
covariance matrix when preliminary estimates are obtained.
The default is SINGULAR=1E-7.

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