A Practical Interval Estimation Method for Spectral Density Function
针对谱密度非参数区间估计中卡方近似和频域自助法覆盖精度低、对参数敏感的问题，提出结合经验似然与频域自助法的混合方法，在温和条件下适用于线性和非线性时间序列，模拟显示新方法覆盖精度好且对带宽不敏感。
The spectral density function can play a key role in time series analysis, where nonparametric interval estimation of the spectral density is a fundamental issue. However, the prevailing pointwise interval methods for spectral densities, including chi-square approximation and frequency domain bootstrap (FDB), can be misleading in practice, perhaps more so than appreciated, as confidence intervals often exhibit low coverage accuracy as well as high sensitivity to tuning parameters. To provide a practical alternative, we propose a new hybrid method that combines the strengths of empirical likelihood (EL) and FDB. The method involves developing an EL statistic for spectral density inference along with a corresponding bootstrap approximation under time dependence, where we allow for general time processes as well as for two different types of kernel smoothing found in application (so-called A- or K-windows). Such windows require differing theories and implementations in practice. As an advantage, the FDB-EL procedure is formally valid under mild conditions for application to a broad range of processes, including both linear and nonlinear time series. Simulation studies demonstrate that FDB-EL-based confidence intervals are effective compared to other methods, as intervals maintain good coverage accuracy while being less sensitive to bandwidth parameters. The confidence interval procedure is illustrated with an application to studying the wind spectrum. Extension to simultaneous confidence intervals has also been discussed.