Various nonparametric kernel regression estimators are presented, based on
which we consider two nonparametric tests for neglected nonlinearity in tim
e series regression models. One of them is the goodness-of-fit test of Cai,
Fan and Yao (2000) and another is the nonparametric conditional moment tes
t by Li and Wang(1998) and Zheng(1996). Bootstrap procedures are used for t
hese tests and their performance is examined via monte carlo experiments, e
specially with conditionally heteroskedastic errors.