Fixed-b asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators
Vogelsang, Timothy J.
University of Exeter
Michigan State University
Journal of Time Series Analysis
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.
Pre-print; author's draft dated February 10, 2007. The definitive version is available at http://www3.interscience.wiley.com/
Journal of Time Series Analysis, Vol. 29, Issue 1, pp. 142-162