ARIMA Procedure

specifies the alternative parameterization of the overall scale of transfer functions in the model. For more information, see the section Alternative Model Parameterization.

specifies input variables and their transfer functions.

The variables in 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:

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. For more information, see the section Specifying Inputs and Transfer Functions.

specifies the estimation method to use. You can specify the following values:

For more information, see the section Estimation Details. By default, METHOD=CLS.

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

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.

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.

specifies the autoregressive part of the model. By default, no autoregressive parameters are fit.

P=(l , l , …, l ) 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

plots the residual autocorrelation functions. The sample autocorrelation, the sample inverse autocorrelation, and the sample partial autocorrelation functions of the model residuals are plotted.

specifies the moving-average part of the model. By default, no moving-average part is included in the model.

Q=(l , l , …, l ) 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.

specifies the type of test statistic that is used in the white noise test of the series when the series contains missing values. You can specify the following values:

By default, WHITENOISE=ST.

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. For a description of the OUTEST= output data set, see the section OUTEST= Data Set.

writes the correlations of the parameter estimates to the OUTEST= data set.

writes the covariances of the parameter estimates to the OUTEST= 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. For a description of the OUTMODEL= output data set, see the section OUTMODEL= 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. For a description of the OUTSTAT= output data set, see the section OUTSTAT= Data Set.

lists starting values for the autoregressive parameters. For more information, see the section Initial Values.

specifies starting values for the parameters in the transfer function parts of the model. For more information, see the section Initial Values.

lists starting values for the moving-average parameters. For more information, see the section Initial Values.

specifies the MU parameter.

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 want to generate forecasts that correspond to a published model.)

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.

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=0.001.

specifies the perturbation value for computing numerical derivatives. The default is DELTA=0.001.

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 can 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.

controls the spacing in the grid printed by the GRID option. The default is GRIDVAL=0.005.

specifies the maximum number of iterations allowed. The default is MAXITER=50.

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. For more information, see the section Estimation Details.

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. For more information, see the section Stationarity and Invertibility.

prints preliminary estimation results and the iterations in the final estimation process.

specifies that the parameter estimates for the denominator polynomial of the transfer function part of the model not be restricted to the stability region. For more information, see the section Stationarity and Invertibility.

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.