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Seasonal adjustment subject to accounting constraints


  • Tucker McElroy


The indirect seasonal adjustment obtained by aggregating component seasonal adjustments may be inadequate, whereas the direct adjustment of the aggregate can typically be ensured to be adequate by adjusting the statistical model. Reconciliation techniques can be used to allocate the discrepancies between the direct and indirect adjustments of the aggregate unto the various component series, essentially enforcing that the indirect procedure yields the same outcome as the adequate direct procedure. This paper proposes utilizing adequacy of the component seasonal adjustments—given the modifications entailed by reconciliation—as an additional constraint to the accounting problem. We focus on seasonal adjustments arising from X‐13ARIMA‐SEATS and apply this constrained reconciliation procedure to copper imports, a component of gross domestic product.

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  • Tucker McElroy, 2018. "Seasonal adjustment subject to accounting constraints," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(4), pages 574-589, November.
  • Handle: RePEc:bla:stanee:v:72:y:2018:i:4:p:574-589
    DOI: 10.1111/stan.12161

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    References listed on IDEAS

    1. Maravall, Agustin, 2006. "An application of the TRAMO-SEATS automatic procedure; direct versus indirect adjustment," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2167-2190, May.
    2. Tucker McElroy, 2017. "Multivariate Seasonal Adjustment, Economic Identities, and Seasonal Taxonomy," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 611-625, October.
    3. Hyndman, Rob J. & Ahmed, Roman A. & Athanasopoulos, George & Shang, Han Lin, 2011. "Optimal combination forecasts for hierarchical time series," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2579-2589, September.
    4. 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.
    5. Tommaso Di Fonzo & Marco Marini, 2011. "Simultaneous and two‐step reconciliation of systems of time series: methodological and practical issues," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 60(2), pages 143-164, March.
    6. Baoline Chen, 2012. "A Balanced System of U.S. Industry Accounts and Distribution of the Aggregate Statistical Discrepancy by Industry," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(2), pages 202-211, February.
    7. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 169-177, April.
    8. Tim Mahedy & Daniel J. Wilson & Glenn D. Rudebusch, 2015. "The puzzle of weak first-quarter GDP growth," FRBSF Economic Letter, Federal Reserve Bank of San Francisco.
    9. Richard Stone & D. G. Champernowne & J. E. Meade, 1942. "The Precision of National Income Estimates," Review of Economic Studies, Oxford University Press, vol. 9(2), pages 111-125.
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