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Spectral analysis characterises oscillatory time series behaviours such ascycles, but accurate estimation requires reasonable numbers of observations.Current COVID-19 time series for many countries are short: pre- andpost-lockdown series are shorter still. Accurate estimation of potentiallyinteresting cycles within such series seems beyond reach. We solve the problemof obtaining accurate estimates from short time series by using recent Bayesianspectral fusion methods. Here we show that transformed new daily COVID-19 casesfor many countries generally contain three cycles operating at wavelengths ofaround 2.7, 4.1 and 6.7 days (weekly). We show that the shorter cycles aresuppressed after lockdown. The pre- and post lockdown differences suggest thatthe weekly effect is at least partly due to non-epidemic factors, whereas thetwo shorter cycles seem intrinsic to the epidemic. Unconstrained, new casesgrow exponentially, but the internal cyclic structure causes periodic falls incases. This suggests that lockdown success might only be indicated by four ormore daily falls in cases. Spectral learning for epidemic time seriescontributes to the understanding of the epidemic process, helping evaluateinterventions and assists with forecasting. Spectral fusion is a generaltechnique that is able to fuse spectra recorded at different sampling rates,which can be applied to a wide range of time series from many disciplines.

Rapidly evaluating lockdown strategies using spectral analysis: the cycles behind new daily COVID-19 cases and what happens after lockdown