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Monitoring the pandemic: A fractional filter for the COVID-19 contact rate

Author

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  • Tobias Hartl
Abstract
This paper aims to provide reliable estimates for the COVID-19 contact rate of a Susceptible-Infected-Recovered (SIR) model. From observable data on confirmed, recovered, and deceased cases, a noisy measurement for the contact rate can be constructed. To filter out measurement errors and seasonality, a novel unobserved components (UC) model is set up. It specifies the log contact rate as a latent, fractionally integrated process of unknown integration order. The fractional specification reflects key characteristics of aggregate social behavior such as strong persistence and gradual adjustments to new information. A computationally simple modification of the Kalman filter is introduced and is termed the fractional filter. It allows to estimate UC models with richer long-run dynamics, and provides a closed-form expression for the prediction error of UC models. Based on the latter, a conditional-sum-of-squares (CSS) estimator for the model parameters is set up that is shown to be consistent and asymptotically normally distributed. The resulting contact rate estimates for several countries are well in line with the chronology of the pandemic, and allow to identify different contact regimes generated by policy interventions. As the fractional filter is shown to provide precise contact rate estimates at the end of the sample, it bears great potential for monitoring the pandemic in real time.

Suggested Citation

  • Tobias Hartl, 2021. "Monitoring the pandemic: A fractional filter for the COVID-19 contact rate," Papers 2102.10067, arXiv.org.
    • Handle: RePEc:arx:papers:2102.10067
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    References listed on IDEAS

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    1. Shimotsu, Katsumi, 2010. "Exact Local Whittle Estimation Of Fractional Integration With Unknown Mean And Time Trend," Econometric Theory, Cambridge University Press, vol. 26(2), pages 501-540, April.
    2. Liu, Laura & Moon, Hyungsik Roger & Schorfheide, Frank, 2021. "Panel forecasts of country-level Covid-19 infections," Journal of Econometrics, Elsevier, vol. 220(1), pages 2-22.
    3. Morten Ørregaard Nielsen, 2015. "Asymptotics for the Conditional-Sum-of-Squares Estimator in Multivariate Fractional Time-Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 154-188, March.
    4. Diebold, Francis X & Rudebusch, Glenn D, 1991. "Is Consumption Too Smooth? Long Memory and the Deaton Paradox," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 1-9, February.
    5. James C. Morley & Charles R. Nelson & Eric Zivot, 2003. "Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 235-243, May.
    6. Tschernig, Rolf & Weber, Enzo & Weigand, Roland, 2013. "Fractionally Integrated VAR Models with a Fractional Lag Operator and Deterministic Trends: Finite Sample Identification and Two-step Estimation," University of Regensburg Working Papers in Business, Economics and Management Information Systems 471, University of Regensburg, Department of Economics.
    7. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-1167, July.
    8. Johansen, Søren & Nielsen, Morten Ørregaard, 2010. "Likelihood inference for a nonstationary fractional autoregressive model," Journal of Econometrics, Elsevier, vol. 158(1), pages 51-66, September.
    9. Korolev, Ivan, 2021. "Identification and estimation of the SEIRD epidemic model for COVID-19," Journal of Econometrics, Elsevier, vol. 220(1), pages 63-85.
    10. Oh, Kum Hwa & Zivot, Eric & Creal, Drew, 2008. "The relationship between the Beveridge-Nelson decomposition and other permanent-transitory decompositions that are popular in economics," Journal of Econometrics, Elsevier, vol. 146(2), pages 207-219, October.
    11. Peter M Robinson, 2006. "Conditional-Sum-of-Squares Estimation ofModels for Stationary Time Series with Long Memory," STICERD - Econometrics Paper Series 505, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    12. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-227, June.
    13. Lee, Sokbae & Liao, Yuan & Seo, Myung Hwan & Shin, Youngki, 2021. "Sparse HP filter: Finding kinks in the COVID-19 contact rate," Journal of Econometrics, Elsevier, vol. 220(1), pages 158-180.
    14. Daron Acemoglu & Victor Chernozhukov & Iván Werning & Michael D. Whinston, 2021. "Optimal Targeted Lockdowns in a Multigroup SIR Model," American Economic Review: Insights, American Economic Association, vol. 3(4), pages 487-502, December.
    15. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
    16. Peter K. Clark, 1987. "The Cyclical Component of U. S. Economic Activity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(4), pages 797-814.
    17. Hortaçsu, Ali & Liu, Jiarui & Schwieg, Timothy, 2021. "Estimating the fraction of unreported infections in epidemics with a known epicenter: An application to COVID-19," Journal of Econometrics, Elsevier, vol. 220(1), pages 106-129.
    18. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    19. Chernozhukov, Victor & Kasahara, Hiroyuki & Schrimpf, Paul, 2021. "Causal impact of masks, policies, behavior on early covid-19 pandemic in the U.S," Journal of Econometrics, Elsevier, vol. 220(1), pages 23-62.
    20. Robinson, Peter, 2006. "Conditional-sum-of-squares estimation of models for stationary time series with long memory," LSE Research Online Documents on Economics 4536, London School of Economics and Political Science, LSE Library.
    21. Felbermayr Gabriel & Hinz Julian & Chowdhry Sonali, 2021. "Après-ski: The spread of coronavirus from Ischgl through Germany," German Economic Review, De Gruyter, vol. 22(4), pages 415-446, November.
    22. Christopher Avery & William Bossert & Adam Clark & Glenn Ellison & Sara Fisher Ellison, 2020. "An Economist's Guide to Epidemiology Models of Infectious Disease," Journal of Economic Perspectives, American Economic Association, vol. 34(4), pages 79-104, Fall.
    23. Tobias Hartl & Rolf Tschernig & Enzo Weber, 2020. "Fractional trends and cycles in macroeconomic time series," Papers 2005.05266, arXiv.org, revised May 2020.
    24. Robert S. Pindyck, 2020. "COVID-19 and the Welfare Effects of Reducing Contagion," NBER Working Papers 27121, National Bureau of Economic Research, Inc.
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