Fixed-b Asymptotic Approximation of the Sampling Behaviour of Nonparametric Spectral Density Estimators
提出一种新的渐近逼近方法，用于分析协方差平稳时间序列谱密度非参数估计量的抽样行为，假设截断滞后为样本量的固定比例，并发现零频率估计量的极限分布依赖于均值估计方式。
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.