Template-Type: ReDIF-Paper 1.0 Author-Name: Min Seong Kim Author-X-Name-First: Min Seong Author-X-Name-Last: Kim Author-Email: minseong.kim@economics.ryerson.ca Author-Workplace-Name: Department of Economics, Ryerson University, Toronto, Canada Author-Name: Yixiao Sun Author-X-Name-First: Yixiao Author-X-Name-Last: Sun Author-Email: yisun@ucsd.edu Author-Workplace-Name: Department of Economics, UC San Diego Author-Name: Jingjing Yang Author-X-Name-First: Jingjing Author-X-Name-Last: Yang Author-Email: jingjingy@unr.edu Author-Workplace-Name: University of Nevada, Reno, NV Title: A Fixed-bandwidth View of the Pre-asymptotic Inference for Kernel Smoothing with Time Series Data Abstract: This paper develops robust testing procedures for nonparametric kernel methods in the presence of temporal dependence of unknown forms. Based on the ?fixed-bandwidth asymptotic variance and the pre-asymptotic variance, we propose a heteroskedasticity and autocorrelation robust (HAR) variance estimator that achieves double robustness ? it is asymptotically valid regardless of whether the temporal dependence is present or not, and whether the kernel smoothing bandwidth is held constant or allowed to decay with the sample size. Using the HAR variance estimator, we construct the studentized test statistic and examine its asymptotic properties under both the fi?xed-smoothing and increasing-smoothing asymptotics. The ?fixed-smoothing approximation and the associated convenient t-approximation achieve extra robustness ? it is asymptotically valid regardless of whether the truncation lag parameter governing the covariance weighting grows at the same rate as or a slower rate than the sample size. Finally, we suggest a simulation-based calibration approach to choose smoothing parameters that optimize testing oriented criteria. Simulation shows that the proposed procedures work very well in ?finite samples. Classification-JEL: C12, C14, C22. Keywords: heteroskedasticity and autocorrelation robust variance, calibration, fi?xed-smoothing asymptotics, ?fixed-bandwidth asymptotics, kernel density estimator, local polynomial estimator, t-approximation, testing-optimal smoothing-parameters choice, temporal dependence Length: 50 pages Creation-Date: 2015-09 Number: 049 File-URL: http://economics.ryerson.ca/workingpapers/wp049.pdf File-Format: Application/pdf Handle: RePEc:rye:wpaper:wp049