Abstract: We propose a new nonparametric method for testing the parametric form of a regression function in the presence of time series errors. The 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 nonparametric 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.
Key words and phrases: Bootstrap, correlated errors, goodness-of-fit test, lack-of-fit test, nearest-neighbor windows, nonparametric regression, residual, time-series errors, trend.