AN IMPROVED GENERALIZED SPECTRAL TEST FOR CONDITIONAL MEAN MODELS IN TIME SERIES WITH CONDITIONAL HETEROSKEDASTICITY OF UNKNOWN FORM

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-