Fixed-b asymptotics for the studentized mean from time series with short, long or negative memory
This paper considers the problem of distribution estimation for the studentized sample mean in the context of Long Memory and Negative Memory time series dynamics, adopting the fixed-bandwidth approach now popular in the econometrics literature. The distribution theory complements the Short Memory results of Kiefer and Vogelsang (2005). In particular, our results highlight the dependence on the employed kernel, whether or not the taper is nonzero at the boundary, and most importantly whether or not the process has short memory. We also demonstrate that small-bandwidth approaches fail when long memory or negative memory is present since the limiting distribution is either a point mass at zero or degenerate. Extensive numerical work provides approximations to the quantiles of the asymptotic distribution for a range of tapers and memory parameters; these quantiles can be used in practice for the construction of confidence intervals and hypothesis tests for the mean of the time series.
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- Nicholas M. Kiefer & Timothy J. Vogelsang & Helle Bunzel, 2000.
"Simple Robust Testing of Regression Hypotheses,"
Econometric Society, vol. 68(3), pages 695-714, May.
- Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005.
"A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests,"
Cambridge University Press, vol. 21(06), pages 1130-1164, December.
- Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory for Heteroskedasticity-Autocorrelation Robust Tests," Working Papers 05-08, Cornell University, Center for Analytic Economics.
- Hurvich, Clifford M., 2002. "Multistep forecasting of long memory series using fractional exponential models," International Journal of Forecasting, Elsevier, vol. 18(2), pages 167-179.
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