The VARMAX Procedure
- Overview
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Getting Started
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Syntax
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DetailsMissing ValuesVARMAX ModelDynamic Simultaneous Equations ModelingImpulse Response FunctionForecastingTentative Order SelectionVAR and VARX ModelingBayesian VAR and VARX ModelingVARMA and VARMAX ModelingModel Diagnostic ChecksCointegrationVector Error Correction ModelingI(2) ModelMultivariate GARCH ModelingOutput Data SetsOUT= Data SetOUTEST= Data SetOUTHT= Data SetOUTSTAT= Data SetPrinted OutputODS Table NamesODS GraphicsComputational Issues
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Examples
- References
Computational Issues
Computational Method
The VARMAX procedure uses numerous linear algebra routines and frequently uses the sweep operator (Goodnight 1979) and the Cholesky root (Golub and Van Loan 1983).
In addition, the VARMAX procedure uses the nonlinear optimization (NLO) subsystem to perform nonlinear optimization tasks for the maximum likelihood estimation. The optimization requires intensive computation.
Convergence Problems
For some data sets, the computation algorithm can fail to converge. Nonconvergence can result from a number of causes, including flat or ridged likelihood surfaces and ill-conditioned data.
If you experience convergence problems, the following points might be helpful:
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Data that contain extreme values can affect results in PROC VARMAX. Rescaling the data can improve stability.
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Changing the TECH=, MAXITER=, and MAXFUNC= options in the NLOPTIONS statement can improve the stability of the optimization process.
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Specifying a different model that might fit the data more closely and might improve convergence.
Memory
Let 
be the length of each series, 
be the number of dependent variables, 
be the order of autoregressive terms, and 
be the order of moving-average terms. The number of parameters to estimate for a VARMA(
) model is
![\[ k + (p+q)k^{2} + k*(k+1)/2 \]](images/etsug_varmax1255.png){kind=small} |
As increases, the number of parameters to estimate increases very quickly. Furthermore the memory requirement for VARMA() quadratically increases as and increase.
For a VARMAX(
) model and GARCH-type multivariate conditional heteroscedasticity models, the number of parameters to estimate and the memory
requirements are considerable.