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复杂振荡时间序列的频率检测与变点估计AI 解读

We consider detecting the evolutionary oscillatory pattern of a signal when it is contaminated by nonstationary 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…

同步压缩变换的渐近分析：面向非线性时频分析的统计推断AI 解读

We provide a statistical analysis of a tool in nonlinear-type time-frequency analysis, the synchrosqueezing transform (SST), for both the null and nonnull cases. The intricate nonlinear interaction of different quantities in SST is quantified by carefully analyzing relevant multivariate complex Gaussian random variables. Specifically, we provide the quotient distribution of dependent and improper complex Gaussian random variables. Then a central limit theorem result for SST…

异方差相关误差下动态周期与趋势的非参数自适应建模AI 解读

Summary Periodicity and trend are features describing an observed sequence, and extracting these features is an important issue in many scientific fields. However, it is not an easy task for existing methods to analyse simultaneously the trend and dynamics of the periodicity such as time varying frequency and amplitude, and the adaptivity of the analysis to such dynamics and robustness to heteroscedastic dependent errors are not guaranteed. These tasks become even more…