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Time Series Modelling of Daily Tax Revenues

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  • Siem Jan Koopman
  • Marius Ooms

Abstract

We provide a detailed discussion of time series modelling of daily data in general and daily tax revenues in particular. The main feature of the daily tax revenue series is the pattern within calendar months. Standard time series methods for seasonal adjustment and forecasting cannot be used since the number of banking days per calendar month varies and because there are two levels of seasonality: between months and within months. We propose a daily time series model based on unobserved components that allows for the classic decomposition into trend, seasonal plus irregular, but it also includes components for intra‐monthly, trading‐day and length‐of‐month effects. Such components typically rely on stochastic cubic spline, polynomial and dummy variable functions. State space techniques are used for the recursive computation of the likelihood and forecasts functions with special allowance for irregular spacing. The model is operational for daily forecasting at the Dutch Ministry of Finance. We present the model specification and discuss estimation and forecasting results up to December 1999. A comparative forecast evaluation is also presented.

Suggested Citation

  • Siem Jan Koopman & Marius Ooms, 2003. "Time Series Modelling of Daily Tax Revenues," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(4), pages 439-469, November.
    • Handle: RePEc:bla:stanee:v:57:y:2003:i:4:p:439-469
    DOI: 10.1111/1467-9574.00239
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    1. Harvey, Andrew & Koopman, Siem Jan & Riani, Marco, 1997. "The Modeling and Seasonal Adjustment of Weekly Observations," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(3), pages 354-368, July.
    2. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    3. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
    4. Ooms, M. & Franses, Ph.H.B.F., 1998. "A seasonal periodic long memory model for monthly river flows," Econometric Institute Research Papers EI 9842, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. A. I. McLeod, 1994. "Diagnostic Checking Of Periodic Autoregression Models With Application," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(2), pages 221-233, March.
    6. Harvey, Andrew C & Koopman, Siem Jan, 1992. "Diagnostic Checking of Unobserved-Components Time Series Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 377-389, October.
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    Cited by:

    1. Alberto Cabrero & Gonzalo Camba-Mendez & Astrid Hirsch & Fernando Nieto, 2009. "Modelling the daily banknotes in circulation in the context of the liquidity management of the European Central Bank," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(3), pages 194-217.
    2. Clive G. Bowsher & Roland Meeks, 2006. "High Dimensional Yield Curves: Models and Forecasting," OFRC Working Papers Series 2006fe11, Oxford Financial Research Centre.
    3. Barend Abeln & Jan P. A. M. Jacobs, 2023. "COVID-19 and Seasonal Adjustment," SpringerBriefs in Economics, in: Seasonal Adjustment Without Revisions, chapter 0, pages 53-61, Springer.
    4. Barend Abeln & Jan P. A. M. Jacobs, 2023. "Seasonal Adjustment of Daily Data with CAMPLET," SpringerBriefs in Economics, in: Seasonal Adjustment Without Revisions, chapter 0, pages 63-78, Springer.
    5. Ollech, Daniel, 2018. "Seasonal adjustment of daily time series," Discussion Papers 41/2018, Deutsche Bundesbank.
    6. Robert Ambrisko, 2022. "Nowcasting Macroeconomic Variables Using High-Frequency Fiscal Data," Working Papers 2022/5, Czech National Bank.
    7. Guglielmo Maria Caporale & Silvia García Tapia & Luis Alberiko Gil-Alana, 2024. "Persistence in Tax Revenues: Evidence from Some OECD Countries," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 22(2), pages 475-491, June.
    8. Koopman, Siem Jan & Ooms, Marius, 2006. "Forecasting daily time series using periodic unobserved components time series models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 885-903, November.
    9. Bowsher, Clive G. & Meeks, Roland, 2008. "The Dynamics of Economic Functions: Modeling and Forecasting the Yield Curve," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1419-1437.
    10. Eliana González & Luis F. Melo & Luis E. Rojas & Brayan Rojas, 2011. "Estimations of the Natural Rate of Interest in Colombia," Money Affairs, CEMLA, vol. 0(1), pages 33-75, January-J.
    11. Alberto Cabrero & Gonzalo Camba-Mendez & Astrid Hirsch & Fernando Nieto, 2009. "Modelling the daily banknotes in circulation in the context of the liquidity management of the European Central Bank," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(3), pages 194-217.
    12. Webel, Karsten, 2022. "A review of some recent developments in the modelling and seasonal adjustment of infra-monthly time series," Discussion Papers 31/2022, Deutsche Bundesbank.

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