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.