Non-parametric and adaptive modelling of dynamic periodicity and trend with heteroscedastic and dependent errors

Yu Chun Chen, Ming Yen Cheng, Hau Tieng Wu

Research output: Contribution to journalArticlepeer-review


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 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 and herpes zoster in Taiwan and respiratory signals observed from a sleep study are analysed.

Original languageEnglish (US)
Pages (from-to)651-682
Number of pages32
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Issue number3
StatePublished - Jun 2014


  • 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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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