On the use of the cumulant generating function for inference on time series
本文提出了基于累积量生成函数的时间序列推断新方法，涵盖密度近似和复合假设检验，扩展了鞍点检验的适用性并保持数值精度，通过模拟和真实数据展示了优势。
Innovative inference procedures for analyzing time series data are introduced. The methodology covers density approximation and composite hypothesis testing based on Whittle's estimator, which is a widely applied M-estimator in the frequency domain. Its core feature involves the cumulant generating function of Whittle's score obtained using an approximated distribution of the periodogram ordinates. A testing algorithm not only significantly expands the applicability of the state-of-the-art saddlepoint test, but also maintains the numerical accuracy of the saddlepoint approximation. Connections are made with three other prevalent frequency domain techniques: the bootstrap, empirical likelihood, and exponential tilting. Numerical examples using both simulated and real data illustrate the advantages and accuracy of the saddlepoint methods.