Department of Mathematics, Imperial College, Huxley Building, 180 Queen's Gate, London, SW7 2AZ, UK.
Sci Rep. 2020 Dec 17;10(1):22134. doi: 10.1038/s41598-020-79092-6.
Spectral analysis characterises oscillatory time series behaviours such as cycles, but accurate estimation requires reasonable numbers of observations. At the time of writing, COVID-19 time series for many countries are short: pre- and post-lockdown series are shorter still. Accurate estimation of potentially interesting cycles seems beyond reach with such short series. We solve the problem of obtaining accurate estimates from short series by using recent Bayesian spectral fusion methods. We show that transformed daily COVID-19 cases for many countries generally contain three cycles operating at wavelengths of around 2.7, 4.1 and 6.7 days (weekly) and that shorter wavelength cycles are suppressed after lockdown. The pre- and post-lockdown differences suggest that the weekly effect is at least partly due to non-epidemic factors. Unconstrained, new cases grow exponentially, but the internal cyclic structure causes periodic declines. This suggests that lockdown success might only be indicated by four or more daily falls. Spectral learning for epidemic time series contributes to the understanding of the epidemic process and can help evaluate interventions. Spectral fusion is a general technique that can fuse spectra recorded at different sampling rates, which can be applied to a wide range of time series from many disciplines.
谱分析可以描述振荡时间序列的行为，如周期，但准确的估计需要合理数量的观测值。在撰写本文时，许多国家的 COVID-19 时间序列都很短：封锁前后的时间序列更短。对于如此短的时间序列，似乎无法准确估计潜在有趣的周期。我们通过使用最近的贝叶斯谱融合方法解决了从短序列中获得准确估计的问题。我们表明，许多国家的每日 COVID-19 病例的转换通常包含三个周期，其波长约为 2.7、4.1 和 6.7 天（每周），并且封锁后较短波长的周期受到抑制。封锁前后的差异表明，每周效应至少部分是由于非疫情因素造成的。不受限制的情况下，新病例呈指数增长，但内部周期性结构导致周期性下降。这表明，只有四次或更多的每日下降才能表明封锁成功。对疫情时间序列的谱学习有助于理解疫情过程，并有助于评估干预措施。谱融合是一种通用技术，可以融合在不同采样率下记录的谱，可应用于来自多个学科的广泛的时间序列。
