Estimated Covid-19 burden in Spain: ARCH underreported non-stationary time series

The problem of dealing with misreported data is very common in a wide range of contexts for different reasons. The current situation caused by the Covid-19 worldwide pandemic is a clear example, where the data provided by official sources were not always reliable due to data collection issues and to the high proportion of asymptomatic cases. In this work, a flexible framework is proposed, with the objective of quantifying the severity of misreporting in a time series and reconstructing the most likely evolution of the process. The performance of Bayesian Synthetic Likelihood to estimate the parameters of a model based on AutoRegressive Conditional Heteroskedastic time series capable of dealing with misreported information and to reconstruct the most likely evolution of the phenomenon is assessed through a comprehensive simulation study and illustrated by reconstructing the weekly Covid-19 incidence in each Spanish Autonomous Community. Only around 51% of the Covid-19 cases in the period 2020/02/23-2022/02/27 were reported in Spain, showing relevant differences in the severity of underreporting across the regions. The proposed methodology provides public health decision-makers with a valuable tool in order to improve the assessment of a disease evolution under different scenarios. The online version contains supplementary material available at 10.1186/s12874-023-01894-9.