We consider detecting the evolutionary oscillatory pattern of a signal when it is contaminated by non-stationary noises with complexly time-varying data generating mechanism. A high-dimensional dense progressive periodogram test is proposed to accurately detect all oscillatory frequencies. A further phase-adjusted local change point detection algorithm is applied in the frequency domain to detect the locations at which the oscillatory pattern changes. Our method is shown to be able to detect all oscillatory frequencies and the corresponding change points within an accurate range with a prescribed probability asymptotically. This study is motivated by oscillatory frequency estimation and change point detection problems encountered in physiological time series analysis. An application to spindle detection and estimation in sleep EEG data is used to illustrate the usefulness of the proposed methodology. A Gaussian approximation scheme and an overlapping-block multiplier bootstrap methodology for sums of complex-valued high dimensional non-stationary time series without variance lower bounds are established, which could be of independent interest.

翻译：我们考虑在数据生成机制呈复杂时变的非平稳噪声干扰下，检测信号的演化振荡模式。本文提出一种高维密集渐进周期图检验方法，可精确检测所有振荡频率。进一步地，我们应用相位调整的局部变点检测算法于频域，以识别振荡模式发生变化的时刻。理论证明，该方法能以给定概率渐近地检测所有振荡频率及相应变点位置，且检测范围精确。本研究受生理时间序列分析中振荡频率估计与变点检测问题的启发，并通过睡眠脑电数据中的纺锤波检测与估计实例展示了所提方法的应用价值。此外，我们还建立了针对复值高维非平稳时间序列和（无需方差下界）的高斯逼近方案与重叠块乘子自助法，该成果可能具有独立的研究意义。