Fixed‐b asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators

Abstract

Abstract. 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.