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Seasonality in High Frequency Time Series

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  • Proietti, Tommaso
  • Pedregal, Diego J.

Abstract

Time series observed at higher frequencies than monthly frequency display complex seasonal patterns that result from the combination of multiple seasonal patterns (with annual, monthly, weekly and daily periodicities) and varying periods, due to the irregularity of the calendar. Seasonality in high frequency data is modelled from two main perspectives: the stochastic harmonic approach, based on the Fourier representation of a periodic function, and the time-domain random effects approach. An encompassing representation illustrates the conditions under which they are equivalent. Three major challenges are considered: the first deals with modelling the effect of moving festivals, holidays and other breaks due to the calendar. Secondly, robust estimation and filtering methods are needed to tackle the level of outlier contamination, which is typically high, due to the lower level of temporal aggregation and the raw nature of the data. Finally, model selection strategies play an important role, as the number of harmonic or random components that are needed to account for the complexity of seasonality can be very large.

Suggested Citation

  • Proietti, Tommaso & Pedregal, Diego J., 2023. "Seasonality in High Frequency Time Series," Econometrics and Statistics, Elsevier, vol. 27(C), pages 62-82.
    • Handle: RePEc:eee:ecosta:v:27:y:2023:i:c:p:62-82
    DOI: 10.1016/j.ecosta.2022.02.001
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    1. Harvey, Andrew, 2001. "Testing in Unobserved Components Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(1), pages 1-19, January.
    2. Marczak, Martyna & Proietti, Tommaso, 2016. "Outlier detection in structural time series models: The indicator saturation approach," International Journal of Forecasting, Elsevier, vol. 32(1), pages 180-202.
    3. Marc K. Francke & Siem Jan Koopman & Aart F. De Vos, 2010. "Likelihood functions for state space models with diffuse initial conditions," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 407-414, November.
    4. [Reference to Proietti], Tommaso, 2000. "Comparing seasonal components for structural time series models," International Journal of Forecasting, Elsevier, vol. 16(2), pages 247-260.
    5. Leschinski, Christian & Sibbertsen, Philipp, 2019. "Model order selection in periodic long memory models," Econometrics and Statistics, Elsevier, vol. 9(C), pages 78-94.
    6. Barr Rosenberg, 1973. "The Analysis of a Cross Section of Time Series by Stochastically Convergent Parameter Regression," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 2, number 4, pages 399-428, National Bureau of Economic Research, Inc.
    7. Busetti, Fabio & Harvey, Andrew, 2003. "Seasonality Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 420-436, July.
    8. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107630024.
    9. Siem Jan Koopman & John A. D. Aston, 2006. "A non-Gaussian generalization of the Airline model for robust seasonal adjustment," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(5), pages 325-349.
    10. 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.
    11. Voges, Michelle & Sibbertsen, Philipp, 2021. "Cyclical fractional cointegration," Econometrics and Statistics, Elsevier, vol. 19(C), pages 114-129.
    12. He, Changli & Kang, Jian & Teräsvirta, Timo & Zhang, Shuhua, 2019. "The shifting seasonal mean autoregressive model and seasonality in the Central England monthly temperature series, 1772–2016," Econometrics and Statistics, Elsevier, vol. 12(C), pages 1-24.
    13. Carlos Santos & David Hendry & Soren Johansen, 2008. "Automatic selection of indicators in a fully saturated regression," Computational Statistics, Springer, vol. 23(2), pages 317-335, April.
    14. Pedregal, Diego J. & Young, Peter C., 2006. "Modulated cycles, an approach to modelling periodic components from rapidly sampled data," International Journal of Forecasting, Elsevier, vol. 22(1), pages 181-194.
    15. 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.
    16. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    17. Jeremy Penzer, 2007. "State space models for time series with patches of unusual observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(5), pages 629-645, September.
    18. Pierce, David A & Grupe, Michael R & Cleveland, William P, 1984. "Seasonal Adjustment of the Weekly Monetary Aggregates: A Model-based Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(3), pages 260-270, July.
    19. Hannan, E J & Terrell, R D & Tuckwell, N E, 1970. "The Seasonal Adjustment of Economic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(1), pages 24-52, February.
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    Cited by:

    1. 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.
    2. 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.

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    More about this item

    Keywords

    State Space Models; Robust filtering; Seasonal Adjustment; Variable selection;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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