Non-parametric and adaptive modelling of dynamic periodicity and trend with heteroscedastic and dependent errors
Yu-Chun Chen, Ming-Yen Cheng, Hau-Tieng Wu
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2014 · Volume 76 · Issue 3
Abstract
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 anddynamicsof the periodicity such as time varying frequency and amplitude, and theadaptivityof the analysis to such dynamics and robustness to heteroscedastic dependent errors are not guaranteed. These tasks become even more challenging when there are multiple periodic components. We propose a non-parametric model to describe the dynamics of multicomponent periodicity and investigate the recently developed synchro-squeezing transform in extracting these features in the presence of a trend and heteroscedastic dependent errors. The identifiability problem of the non-parametric periodicity model is studied, and the adaptivity and robustness properties of the synchro-squeezing transform are theoretically justified in both discrete and continuous time settings. Consequently we have a new technique for decoupling the trend, periodicity and heteroscedastic, dependent error process in a general non-parametric set-up. Results of a series of simulations are provided, and the incidence time series of varicella andherpes zosterin Taiwan and respiratory signals observed from a sleep study are analysed.
Keywords
Auto-regressive moving average errors, Continuous time auto-regressive moving average processes, Cycles, Instantaneous frequency, Non-stationary processes, Periodic functions, Synchro-squeezing transform, Time–frequency analysis
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