COVID-19 Dashboard: Live time-series analysis to monitor and forecast the COVID-19 outbreak in Switzerland

Description of data sources, statistical methods and displayed results

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Description of the data

We extract live time series data describing the COVID-19 outbreak in Switzerland from the following data sources:

• Swiss Federal Office of Public Health (FOPH) situation reports
  • Extracted data: daily new reported cases, new hospitalizations, new fatalities
• corona-data.ch interactive dashboard displaying COVID-19 information for Switzerland. The data available here is aggregated from the data individually released by the Swiss cantons available on the platform of the Specialist Unit for Open Government Data Canton of Zurich, OpenZH
  • Extracted data: daily new reported cases, current hospitalizations, new fatalities

To reduce the noise levels and correct for data reporting or processing delays, before performing downstream analysis or fitting time series models, we applied a 7-day-window smoothing operation on all the time series. On the Monitoring and Forecasting panel, the user has the possibility to visualize the data in either mode: raw or smoothed numbers, respectively.

Time series model

An autoregressive integrated moving average (ARIMA) model [(1)] [references] was fitted to each smoothed time series. The fitted model was then used to make real-time forecasts of the evolution of the time series over the next 7 days. An ARIMA model is formally defined by three order variables \((p,d,q)\), where \(p\) is the autoregressive order and \(q\) is the moving average order. The differencing order \(d\) represents the number of times the time series needs to be differenced in order to be stationary (mean, variance and covariance are constant). After differencing of order \(d\), each differenced observed data point at time \(t\) (denoted by \(X_t^{d}\)) was regressed on \(p\) previously observed data points with an error depending on the errors at \(q\) previous steps: \[X_t^{(d)} = \sum_{i=1}^{p}a_iX_{t-i}^{(d)} + e_t + \sum_{j=1}^{q}b_je_{t-j}\] with \(e_t\) being the error at time \(t\). For given values of \(p\) and \(q\), the coefficients \(a_i\) and \(b_j\) were inferred by maximizing the likelihood of the regression model assuming normally-distributed error terms.

For each time series, ARIMA models were fitted for all the combinations of \(p\) and \(q\) ranging from 1 to 7 and the model with the best Akaike information criterion (AIC) was chosen. The tools available in the package forecast in R [(2)] [references] were used for implementing the model fitting and forecast.

References

(1) Asteriou, Dimitros, and Stephen G. Hall. 2011. “ARIMA Models and the Box–Jenkins Methodology.” Applied Econometrics 2 (2). Palgrave MacMillan Hampshire: 265–86.

(2) Hyndman, Rob J. and Yeasmin Khandakar. 2008, “Automatic time series forecasting: The forecast package for R”. Journal of Statistical Software, 26(3).

COVID-19 Dashboard: Live time-series analysis to monitor and forecast the COVID-19 outbreak in Switzerland

Authors

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The aim of the COVID-19 Dashboard is to provide a tool for real-time monitoring and short-term forecasting of the COVID-19 outbreak in Switzerland based on daily updated time series of various output measurements. The Dashboard presents results from various data-driven statistical analyses modeling the outbreak development without imposing assumptions on the disease transmission dynamics.

This tool was developed by Monica Golumbeanu and Melissa Penny in the Disease and Intervention Dynamics group of Prof. Melissa Penny at the Swiss Tropical and Public Health Institute and University of Basel.

Hosting and computing services are offered by the sciCORE Center for Scientific Computing at the University of Basel.

For questions, suggestions or comments contact monica.golumbeanu@swisstph.ch or melissa.penny@unibas.ch.