A nonparametric test for changing trends

Many tests of parameter change in dynamic models exhibit nonmonotonic power. An important source of the nonmonotonic power comes from the bias in estimating parameters when there is a change in the deterministic component. To avoid this bias, we propose a nonparametric test for changing trends based on nonparametrically detrended data. The tests are similar in spirit to nonparametric conditional moment tests such as Fan and Li (J. Nonparametr. Stat. 10 (1999a) 245; 11 (1999b) 251) and Zheng (J. Econometrics 75 (1996) 263). The resulting statistics have a standard normal distribution. A Monte Carlo experiment suggests that the tests have good power against changes in the deterministic component.