Non-Parametric and Adaptive Modelling of Dynamic Periodicity and Trend with Heteroscedastic and Dependent Errors
异方差相关误差下动态周期与趋势的非参数自适应建模AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要直接研究时间变化的周期、趋势及异方差相关误差，并分析实际时间序列。
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异方差相关误差下动态周期与趋势的非参数自适应建模
- 研究问题
- 研究在异方差且相关的误差背景下，如何同时提取趋势与多个周期成分，并追踪周期频率和振幅随时间的变化。
- 方法与思路
- 作者提出多成分动态周期的非参数模型，研究同步压缩变换在趋势及异方差相关误差存在时的特征提取，并分析模型可识别性。
- 材料陈述的贡献
- 摘要称，在离散与连续时间下论证了变换的自适应性和稳健性，形成分离趋势、周期与误差的技术，并提供模拟及疾病和呼吸信号应用。
- 阅读关注点
- 应核对周期成分可识别的条件、频率与振幅变化的限制、趋势及误差过程假设，并检查离散实现、边界处理和应用中的参数选择。
- 阅读边界
- 仅据所给 Crossref 摘要；理论条件、模拟数值和应用结果未展开，不能认定方法对任意周期重叠或任意相关误差均稳健。
原文摘要
Summary 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.