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

被引:81
作者
Chen, Yu-Chun [1 ]
Cheng, Ming-Yen [2 ]
Wu, Hau-Tieng [3 ]
机构
[1] Natl Yang Ming Univ, Taipei 112, Taiwan
[2] Natl Taiwan Univ, Taipei 10764, Taiwan
[3] Univ Calif Berkeley, Berkeley, CA 94720 USA
基金
美国国家科学基金会;
关键词
Periodic functions; Instantaneous frequency; Time-frequency analysis; Synchro-squeezing transform; Auto-regressive moving average errors; Cycles; Non-stationary processes; Continuous time auto-regressive moving average processes; HERPES-ZOSTER; TIME-SERIES; SEASONAL-VARIATION; VARICELLA VACCINE; SPECTRAL-ANALYSIS; VARIABLE-STARS; IMPACT; TAIWAN; TESTS;
D O I
10.1111/rssb.12039
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
070103 [概率论与数理统计]; 140311 [社会设计与社会创新];
摘要
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.
引用
收藏
页码:651 / 682
页数:32
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