Introduction |

Nonlinear Systems Regression and Simulation |

The MODEL procedure provides parameter estimation, simulation, and forecasting of dynamic nonlinear simultaneous equation models. The MODEL procedure includes the following features:

nonlinear regression analysis for systems of simultaneous equations, including weighted nonlinear regression

full range of parameter estimation methods including the following:

nonlinear ordinary least squares (OLS)

nonlinear seemingly unrelated regression (SUR)

nonlinear two-stage least squares (2SLS)

nonlinear three-stage least squares (3SLS)

iterated SUR

iterated 3SLS

generalized method of moments (GMM)

nonlinear full-information maximum likelihood (FIML)

simulated method of moments (SMM)

supports dynamic multi-equation nonlinear models of any size or complexity

uses the full power of the SAS programming language for model definition, including left-hand-side expressions

hypothesis tests of nonlinear functions of the parameter estimates

linear and nonlinear restrictions of the parameter estimates

bounds imposed on the parameter estimates

computation of estimates and standard errors of nonlinear functions of the parameter estimates

estimation and simulation of ordinary differential equations (ODE’s)

vector autoregressive error processes and polynomial lag distributions easily specified for the nonlinear equations

variance modeling (ARCH, GARCH, and others)

computation of goal-seeking solutions of nonlinear systems to find input values needed to produce target outputs

dynamic, static, or

*n*-period-ahead-forecast simulation modessimultaneous solution or single equation solution modes

Monte Carlo simulation using parameter estimate covariance and across-equation residuals covariance matrices or user-specified random functions

a variety of diagnostic statistics including the following

model R-square statistics

general Durbin-Watson statistics and exact

*p*-valuesasymptotic standard errors and

*t*testsfirst-stage R-square statistics

covariance estimates

collinearity diagnostics

simulation goodness-of-fit statistics

Theil inequality coefficient decompositions

Theil relative change forecast error measures

heteroscedasticity tests

Godfrey test for serial correlation

Hausman specification test

Chow tests

block structure and dependency structure analysis for the nonlinear system

listing and cross-reference of fitted model

automatic calculation of needed derivatives by using exact analytic formula

efficient sparse matrix methods used for model solution; choice of other solution methods

Model definition, parameter estimation, simulation, and forecasting can be performed interactively in a single SAS session or models can also be stored in files and reused and combined in later runs.

Copyright © 2008 by SAS Institute Inc., Cary, NC, USA. All rights reserved.