IDEAS home Printed from https://ideas.repec.org/a/bla/istatr/v90y2022i2p259-284.html
   My bibliography  Save this article

A Review of Seasonal Adjustment Diagnostics

Author

Listed:
  • Tucker McElroy
  • Anindya Roy

Abstract

Seasonal adjustment methods are used to process and publish thousands of time series across the world each month, and judgement of the adequacy relies heavily upon seasonal adjustment diagnostics. This paper discusses tests for the adequacy of a seasonal adjustment, first reviewing the broader background on tests for seasonality and then proceeding to four tests that are appropriate for stationary forms of seasonality. We contrast time‐domain and frequency‐domain approaches, focusing upon four diagnostics available in the seasonal adjustment literature (and software packages) and applying the methods to a large collection of public use time series. Each of the four tests is designed around a distinct formulation of seasonality, and hence, empirical performances differ; we compare and contrast the methods and include discussion on how diagnostic results can be used to improve faulty seasonal adjustments. Directions for future research, involving inverse partial autocorrelations and polyspectra, are also discussed, and the methodologies are supported by theoretical and simulation results.

Suggested Citation

  • Tucker McElroy & Anindya Roy, 2022. "A Review of Seasonal Adjustment Diagnostics," International Statistical Review, International Statistical Institute, vol. 90(2), pages 259-284, August.
    • Handle: RePEc:bla:istatr:v:90:y:2022:i:2:p:259-284
    DOI: 10.1111/insr.12482
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/insr.12482
    Download Restriction: no
    File URL: https://libkey.io/10.1111/insr.12482?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
    2. McElroy Tucker, 2021. "A Diagnostic for Seasonality Based Upon Polynomial Roots of ARMA Models," Journal of Official Statistics, Sciendo, vol. 37(2), pages 367-394, June.
    3. [Reference to Proietti], Tommaso, 2000. "Comparing seasonal components for structural time series models," International Journal of Forecasting, Elsevier, vol. 16(2), pages 247-260.
    4. Hirotugu Akaike, 1980. "Seasonal Adjustment By A Bayesian Modeling," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 1-13, January.
    5. Nigar Hashimzade & Timothy J. Vogelsang, 2008. "Fixed‐b asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 142-162, January.
    6. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 291-320, October.
    7. Tomas del Barrio Castro & Denise R. Osborn, 2004. "The consequences of seasonal adjustment for periodic autoregressive processes," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 307-321, December.
    8. Franses, Philip Hans, 1996. "Recent Advances in Modelling Seasonality," Journal of Economic Surveys, Wiley Blackwell, vol. 10(3), pages 299-345, September.
    9. Canova, Fabio & Hansen, Bruce E, 1995. "Are Seasonal Patterns Constant over Time? A Test for Seasonal Stability," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 237-252, July.
    10. McNulty, Mark S. & Huffman, Wallace E., 1989. "The sample spectrum of time series with trading day variation," Economics Letters, Elsevier, vol. 31(4), pages 367-370, December.
    11. McElroy, Tucker S. & Politis, Dimitris N., 2014. "Spectral density and spectral distribution inference for long memory time series via fixed-b asymptotics," Journal of Econometrics, Elsevier, vol. 182(1), pages 211-225.
    12. Wei Lin & Jianhua Z. Huang & Tucker McElroy, 2020. "Time Series Seasonal Adjustment Using Regularized Singular Value Decomposition," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 487-501, July.
    13. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030.
    14. Ansley, Craig F & Wecker, William E, 1984. "Issues Involved with the Seasonal Adjustment of Economic Time Series: Comment: On Dips in the Spectrum of a Seasonally Adjusted Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 323-324, October.
    15. Ghysels,Eric & Osborn,Denise R., 2001. "The Econometric Analysis of Seasonal Time Series," Cambridge Books, Cambridge University Press, number 9780521565882, September.
    16. Proietti, Tommaso, 1996. "Persistence of Shocks on Seasonal Processes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(4), pages 383-398, July-Aug..
    17. Hylleberg, Svend, 1986. "Seasonality in Regression," Elsevier Monographs, Elsevier, edition 1, number 9780123634559 edited by Shell, Karl.
    18. Gregoir, Stephane, 2006. "Efficient tests for the presence of a pair of complex conjugate unit roots in real time series," Journal of Econometrics, Elsevier, vol. 130(1), pages 45-100, January.
    19. Osborn, Denise R., 1991. "The implications of periodically varying coefficients for seasonal time-series processes," Journal of Econometrics, Elsevier, vol. 48(3), pages 373-384, June.
    20. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Time Series: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 343-349, October.
    21. 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.
    22. Franses, Philip Hans, 1994. "A multivariate approach to modeling univariate seasonal time series," Journal of Econometrics, Elsevier, vol. 63(1), pages 133-151, July.
    23. Sun, Yixiao, 2014. "Let’s fix it: Fixed-b asymptotics versus small-b asymptotics in heteroskedasticity and autocorrelation robust inference," Journal of Econometrics, Elsevier, vol. 178(P3), pages 659-677.
    24. Chris Blakely & Tucker McElroy, 2017. "Signal extraction goodness-of-fit diagnostic tests under model parameter uncertainty: Formulations and empirical evaluation," Econometric Reviews, Taylor & Francis Journals, vol. 36(4), pages 447-467, April.
    25. Osborn, Denise R, 1988. "Seasonality and Habit Persistence in a Life Cycle Model of Consumptio n," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(4), pages 255-266, October-D.
    26. Chen, Rong & Fomby, Thomas B, 1999. "Forecasting with Stable Seasonal Pattern Models with an Application to Hawaiian Tourism Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(4), pages 497-504, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Daniel Dzikowski & Carsten Jentsch, 2024. "Structural Periodic Vector Autoregressions," Papers 2401.14545, arXiv.org.
    2. Fok, D. & Franses, Ph.H.B.F. & Paap, R., 2005. "Performance of Seasonal Adjustment Procedures: Simulation and Empirical Results," Econometric Institute Research Papers EI 2005-30, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Ghysels, E., 1993. "A Time Series Model with Periodic Stochastic Regime Switching," Cahiers de recherche 9314, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    4. Tomás Barrio & Mariam Camarero & Cecilio Tamarit, 2019. "Testing for Periodic Integration with a Changing Mean," Computational Economics, Springer;Society for Computational Economics, vol. 54(1), pages 45-75, June.
    5. Svend Hylleberg, 2006. "Seasonal Adjustment," Economics Working Papers 2006-04, Department of Economics and Business Economics, Aarhus University.
    6. Tomas Barrio Castro & Mariam Camarero & Cecilio Tamarit, 2015. "An analysis of the trade balance for OECD countries using periodic integration and cointegration," Empirical Economics, Springer, vol. 49(2), pages 389-402, September.
    7. Zou, Nan & Politis, Dimitris N., 2021. "Bootstrap seasonal unit root test under periodic variation," Econometrics and Statistics, Elsevier, vol. 19(C), pages 1-21.
    8. McElroy Tucker, 2021. "A Diagnostic for Seasonality Based Upon Polynomial Roots of ARMA Models," Journal of Official Statistics, Sciendo, vol. 37(2), pages 367-394, June.
    9. del Barrio Castro, Tomás & Osborn, Denise R., 2023. "Periodic Integration and Seasonal Unit Roots," MPRA Paper 117935, University Library of Munich, Germany, revised 2023.
    10. Politis, Dimitris, 2016. "HEGY test under seasonal heterogeneity," University of California at San Diego, Economics Working Paper Series qt2q4054kf, Department of Economics, UC San Diego.
    11. Pami Dua & Lokendra Kumawat, 2005. "Modelling and Forecasting Seasonality in Indian Macroeconomic Time Series," Working papers 136, Centre for Development Economics, Delhi School of Economics.
    12. Tomás del Barrio Castro & Gianluca Cubadda & Denise R. Osborn, 2022. "On cointegration for processes integrated at different frequencies," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 412-435, May.
    13. McElroy, Tucker S. & Jach, Agnieszka, 2023. "Identification of the differencing operator of a non-stationary time series via testing for zeroes in the spectral density," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    14. Bollerslev, Tim & Ghysels, Eric, 1996. "Periodic Autoregressive Conditional Heteroscedasticity," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 139-151, April.
    15. Méndez Parra, Maximiliano, 2015. "Futures prices, trade and domestic supply of agricultural commodities," Economics PhD Theses 0115, Department of Economics, University of Sussex Business School.
    16. Mendez Parra, Maximiliano, 2015. "Seasonal Unit Roots and Structural Breaks in agricultural time series: Monthly exports and domestic supply in Argentina," MPRA Paper 63831, University Library of Munich, Germany, revised 06 Apr 2015.
    17. Siem Jan Koopman & Marius Ooms & Irma Hindrayanto, 2009. "Periodic Unobserved Cycles in Seasonal Time Series with an Application to US Unemployment," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(5), pages 683-713, October.
    18. Franses, Philip Hans & van Dijk, Dick, 2005. "The forecasting performance of various models for seasonality and nonlinearity for quarterly industrial production," International Journal of Forecasting, Elsevier, vol. 21(1), pages 87-102.
    19. del Barrio Castro Tomás & Osborn Denise R, 2011. "Nonparametric Tests for Periodic Integration," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-35, February.
    20. Haldrup, Niels & Hylleberg, Svend & Pons, Gabriel & Sanso, Andreu, 2007. "Common Periodic Correlation Features and the Interaction of Stocks and Flows in Daily Airport Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 21-32, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:istatr:v:90:y:2022:i:2:p:259-284. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/isiiinl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.