Fixed-b asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators
We propose a new asymptotic approximation for the sampling behaviour of nonparametric estimators of the spectral density of a covariance stationary time series. According to the standard approach, the truncation lag grows more slowly than the sample size. We derive first-order limiting distributions under the alternative assumption that the truncation lag is a fixed proportion of the sample size. Our results extend the approach of Neave (1970), who derived a formula for the asymptotic variance of spectral density estimators under the same truncation lag assumption. We show that the limiting distribution of zero-frequency spectral density estimators depends on how the mean is estimated and removed. The implications of our zero-frequency results are consistent with exact results for bias and variance computed by Ng and Perron (1996). Finite sample simulations indicate that the new asymptotics provides a better approximation than the standard one. Copyright 2007 The Authors Journal compilation 2007 Blackwell Publishing Ltd.
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Volume (Year): 29 (2008)
Issue (Month): 1 (01)
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References listed on IDEAS
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- Helle Bunzel & Timothy Vogelsang, 2003.
"Powerful Trend Function Tests That are Robust to Strong Serial Correlation with an Application to the Prebisch Singer Hypothesis,"
- Bunzel, Helle & Vogelsang, Timothy J., 2005. "Powerful Trend Function Tests That Are Robust to Strong Serial Correlation, With an Application to the Prebisch-Singer Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 381-394, October.
- Bunzel, Helle & Vogelsang, Timothy J., 2003. "Powerful Trend Function Tests That Are Robust to Strong Serial Correlation with an Application to the Prebisch-Singer Hypothesis," Staff General Research Papers 10353, Iowa State University, Department of Economics.
- Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005.
"A New Asymptotic Theory for Heteroskedasticity-Autocorrelation Robust Tests,"
05-08, Cornell University, Center for Analytic Economics.
- Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1130-1164, December.
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