标题： TFT-bootstrap：在频域重采样时间序列以在时域获得复制样本 显示英文标题

标题： TFT-bootstrap: Resampling time series in the frequency domain to obtain replicates in the time domain

摘要： 提出了一种新的时间序列自助法方案，即时频切换（TFT）自助法。其基本思想是对观测时间序列的傅里叶系数进行自助采样，然后反向变换以在时域中获得自助样本。与之前的相关提议（如“替代数据”方法）相比，后者仅重新取样了傅里叶系数的相位，因此有效性有限。相比之下，我们证明了适当地重取样相位和幅度，并对傅里叶系数进行一定的平滑处理，可以得到一种自助方案，该方案能够模仿一大类时间序列过程的正确二阶矩结构。作为主要结果之一，在各种流行的频率域自助方法下，我们得到了TFT自助法的功能极限定理。TFT自助法的可能应用自然出现在变点分析和单位根检验中，其中统计量通常基于部分和函数。最后，一个小规模模拟研究探索了TFT自助法在小样本中的潜力，结果显示，对于所讨论的变点分析和单位根检验中的测试，如果用大小和功效来衡量，它比相应的渐近检验更能取得良好的结果。 显示英文摘要

摘要： A new time series bootstrap scheme, the time frequency toggle (TFT)-bootstrap, is proposed. Its basic idea is to bootstrap the Fourier coefficients of the observed time series, and then to back-transform them to obtain a bootstrap sample in the time domain. Related previous proposals, such as the "surrogate data" approach, resampled only the phase of the Fourier coefficients and thus had only limited validity. By contrast, we show that the appropriate resampling of phase and magnitude, in addition to some smoothing of Fourier coefficients, yields a bootstrap scheme that mimics the correct second-order moment structure for a large class of time series processes. As a main result we obtain a functional limit theorem for the TFT-bootstrap under a variety of popular ways of frequency domain bootstrapping. Possible applications of the TFT-bootstrap naturally arise in change-point analysis and unit-root testing where statistics are frequently based on functionals of partial sums. Finally, a small simulation study explores the potential of the TFT-bootstrap for small samples showing that for the discussed tests in change-point analysis as well as unit-root testing, it yields better results than the corresponding asymptotic tests if measured by size and power.