Nonparametric test for the form of parametric regression with time series errors

We propose a new nonparametric method for testing the parametric form of a regression function in the presence of time series errors. The nonparametric test is motivated by recent advancement in the theory of ANOVA with large number of factor levels and also utilizes a new difference-based estimation method in non-parametric regression with time-series errors proposed by Hall and Van Keilegom (2003). The test statistic is asymptotically normal under the null and local alternative hypotheses. We also propose a bootstrap method to calculate the critical values and prove its consistency. In a Monte Carlo study, we demonstrate that this bootstrap procedure has good properties for moderate sample size