Valid Inference for a Class of Models Where Standard Inference Performs Poorly; Including Nonlinear Regression, ARMA, GARCH, and Unobserved Components

35 Pages Posted: 23 Sep 2008

See all articles by Jun Ma

Jun Ma

Northeastern University - Department of Economics

Charles R. Nelson

Dept of Economics

Date Written: September 15, 2008

Abstract

Standard inference works poorly in models of the form y=gamma*g(beta,x) epsum, because the standard error for beta_hat depends on gamma_hat. In this paper we show that this problem is usefully studied by working with the linearization of g(.) and the resulting reduced form regression. Bias and dispersion in beta_hat depend on correlation between the 'regressors' and on gamma, as does the size of the t-test. A reduced form test however is exact when g(.) is linear and has nearly correct size in examples from non-linear regression, ARMA, GARCH, and Unobserved Components models. Further, its distribution does not depend on the identifying restriction gamma is not equal to 0.

Keywords: ARMA, Unobserved Components, State Space, GARCH, Zero-Information-Limit-Condition

JEL Classification: C120, C220, C330

Suggested Citation

Ma, Jun and Nelson, Charles R., Valid Inference for a Class of Models Where Standard Inference Performs Poorly; Including Nonlinear Regression, ARMA, GARCH, and Unobserved Components (September 15, 2008). Available at SSRN: https://ssrn.com/abstract=1270227 or http://dx.doi.org/10.2139/ssrn.1270227

Jun Ma

Northeastern University - Department of Economics ( email )

301 Lake Hall
360 Huntington Avenue
Boston, MA MA 02446
United States

Charles R. Nelson (Contact Author)

Dept of Economics ( email )

Box 353330
Seattle, WA 98195-3330
United States

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