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Temporal disaggregation of overlapping noisy quarterly data using state space models: Estimation of monthly business sector output from Value Added Tax data in the UK

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  • Paul Labonne
  • Martin Weale

Abstract

This paper derives monthly estimates of turnover for small and medium size businesses in the UK from rolling quarterly VAT-based turnover data. We develop a state space approach for filtering and temporally disaggregating the VAT figures, which are noisy and exhibit dynamic unobserved components. We notably derive multivariate and nonlinear methods to make use of indicator series and data in logarithms respectively. After illustrating our temporal disaggregation method and estimation strategy using an example industry, we estimate monthly seasonally adjusted figures for the seventy-five industries for which the data are available. We thus produce an aggregate series representing approximately a quarter of gross value added in the economy. We compare our estimates with those derived from the Monthly Business Survey and find that the VAT-based estimates show a different time profile and are less volatile. In addition to this empirical work our contribution to the literature on temporal disaggregation is twofold. First, we provide a discussion of the effect that noise in aggregate figures has on the estimation of disaggregated model components. Secondly, we illustrate a new temporal aggregation strategy suited for overlapping data. The technique we adopt is more parsimonious than the seminal method of Harvey and Pierse (1984) and can easily be generalised to nonoverlapping data.

Suggested Citation

  • Paul Labonne & Martin Weale, 2018. "Temporal disaggregation of overlapping noisy quarterly data using state space models: Estimation of monthly business sector output from Value Added Tax data in the UK," Economic Statistics Centre of Excellence (ESCoE) Discussion Papers ESCoE DP-2018-18, Economic Statistics Centre of Excellence (ESCoE).
    • Handle: RePEc:nsr:escoed:escoe-dp-2018-18
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    References listed on IDEAS

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    1. [Reference to Proietti], Tommaso, 2000. "Comparing seasonal components for structural time series models," International Journal of Forecasting, Elsevier, vol. 16(2), pages 247-260.
    2. Helske, Jouni, 2017. "KFAS: Exponential Family State Space Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 78(i10).
    3. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 127-152, April.
    4. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
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    6. S. J. Koopman & J. Durbin, 2000. "Fast Filtering and Smoothing for Multivariate State Space Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(3), pages 281-296, May.
    7. Tommaso Proietti & Filippo Moauro, 2006. "Dynamic factor analysis with non‐linear temporal aggregation constraints," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 281-300, April.
    8. 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.
    9. Barndorff-Nielsen, O. & Schou, G., 1973. "On the parametrization of autoregressive models by partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 3(4), pages 408-419, December.
    10. J. C. G. Boot & W. Feibes & J. H. C. Lisman, 1967. "Further Methods of Derivation of Quarterly Figures from Annual Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 16(1), pages 65-75, March.
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    Cited by:

    1. Jagjit S. Chadha & Richard Barwell, 2019. "Renewing our Monetary Vows: Open Letters to the Governor of the Bank of England," National Institute of Economic and Social Research (NIESR) Occasional Papers 58, National Institute of Economic and Social Research.

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    More about this item

    Keywords

    Temporal disaggregation; State space models; Structural time series models; Administrative data; Monthly GDP;
    All these keywords.

    JEL classification:

    • E01 - Macroeconomics and Monetary Economics - - General - - - Measurement and Data on National Income and Product Accounts and Wealth; Environmental Accounts
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • P44 - Political Economy and Comparative Economic Systems - - Other Economic Systems - - - National Income, Product, and Expenditure; Money; Inflation

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