# 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 modes

• simultaneous 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-values

• asymptotic standard errors and t tests

• first-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.