  Seasonality (or 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 trend and {\it dynamics} of the seasonality such as
time-varying frequency and amplitude, and the {\it adaptivity} of the analysis
to such dynamics and robustness to heteroscedastic, dependent errors is not
guaranteed. These tasks become even more challenging when there exist multiple
seasonal components. We propose a nonparametric model to describe the dynamics
of multi-component seasonality, and investigate the recently developed
Synchrosqueezing transform (SST) in extracting these features in the presence
of a trend and heteroscedastic, dependent errors. The identifiability problem
of the nonparametric seasonality model is studied, and the adaptivity and
robustness properties of the SST are theoretically justified in both discrete-
and continuous-time settings. Consequently we have a new technique for
de-coupling the trend, seasonality and heteroscedastic, dependent error process
in a general nonparametric setup. Results of a series of simulations are
provided, and the incidence time series of varicella and herpes zoster in
Taiwan and respiratory signals observed from a sleep study are analyzed.
