Valid inference for a class of models where standard inference performs poorly: Including nonlinear regression, ARMA, GARCH, and unobserved components

In models that have a representation of the form       ) , ( x g y the Wald test for ˆBeta has systematically wrong size in finite samples when the indentifying parameter Gamma is small relative to its estimation error. An alternative test based on linearization of g(.) can be interpreted as an approximation to the exact test of Fieller (1954) for a ratio of regression coefficients, or as an LM test in the spirit of Breusch and Pagan (1980)., We show that this test has nearly correct size in non-linear regression, ARMA, GARCH, and Unobserved Components models where the Wald test performs poorly.