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 analyze simultaneously the dynamic periodicity and trend, and the adaptivity of the analysis to such dynamics and robustness to heteroscedastic, dependent errors are not guaranteed. These tasks become even more challenging when there exist multiple periodic components.
We propose a nonparametric model to describe these features, and propose a time-frequency analysis technique called ``synchrosqueezing transform'' (SST) to analyze the model in the presence of a trend and heteroscedastic, dependent errors. The adaptivity and robustness properties of the SST and relevant issues are theoretically justified. Consequently we have a new technique for de-coupling the trend, periodicity and heteroscedastic, dependent error process in a general setup. The model and technique have been applied to different fields ranging from biomedicine, physics to finance. In this talk, we will demonstrate results on several clinical problems including: (1) sleep depth estimation; (2) ventilator weaning prediction; (3) differential effects of the anesthetics on the brain.