Nonparametric Bootstrap Tests for Neglected Nonlinearity in Time Series Regression Models

A unified framework for various nonparametric kernel regression estimators is presented, based on which we consider two nonparametric tests for neglected nonlinearity in time 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 test by Li and Wang (1998) and Zheng (1996). Bootstrap procedures are used for these tests and their performance is examined via monte carlo experiments, especially with conditionally heteroskedastic errors.