Fixed-b Asymptotic Approximation of the Sampling Behavior of Nonparametric Spectral Density Estimators

We propose a new asymptotic approximation for the sampling behavior of nonparametric estimates of the spectral density of a covariance stationary time series. According to the standard approach, the truncation lag grows slower 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 data is demeaned. The implications of our zero frequency results are qualitatively similar to exact results for bias and variance computed by Ng and Perron (1996). Finite sample simulations indicate that new asymptotics provides a better approximation than the standard asymptotics when the bandwidth is not small.