Abstract :
Dynamic economic theories usually have implications on and only on the conditional
mean dynamics of economic processes+ Using a generalized spectral derivative
approach, Hong and Lee ~2005, Review of Economic Studies 72, 499–541!
recently proposed a new class of omnibus nonparametric specification tests for
linear and nonlinear time series conditional mean models, where the dimension
of the conditioning information set may be infinite+ The tests can detect a wide
range of model misspecifications in mean while being robust to conditional heteroskedasticity
and time-varying higher order moments of unknown form+ They
enjoy an asymptotic “nuisance parameter–free” property in the sense that parameter
estimation uncertainty has no impact on the asymptotic N~0,1! distribution
of the test statistics+ As a result, only the estimated residuals from the null parametric
model are needed to implement the tests, and no specific estimation is
required+
Although parameter estimation uncertainty has no impact on the asymptotic
distribution of the tests, it may have significant impact on the finite-sample distribution,
and such an impact may become more substantial as the number of estimated
parameters increases+ In this paper, we adopt the Wooldridge ~1990,
Econometric Theory 6, 17– 43! device for parametric m-tests to the Hong and Lee
~2005! nonparametric tests to reduce the impact of parameter estimation uncer-
