Gaussian Approximation for Lag‐Window Estimators and the Construction of Confidence Bands for the Spectral Density
研究了利用高斯近似为平稳时间序列的谱密度构建同时置信带，验证了乘子自助法的渐近有效性并推导了收敛速度，模拟实验展示了有限样本性质。
ABSTRACT In this article, we consider the construction of simultaneous confidence bands for the spectral density of a stationary time series using a Gaussian approximation for classical lag‐window spectral density estimators evaluated at the set of all positive Fourier frequencies. The Gaussian approximation opens up the possibility to verify asymptotic validity of a multiplier bootstrap procedure and, even further, to derive the corresponding rate of convergence. A small simulation study sheds light on the finite sample properties of this bootstrap proposal.