IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v27y2006i6p877-910.html
   My bibliography  Save this article

Efficient Semiparametric Estimation of the Periods in a Superposition of Periodic Functions with Unknown Shape

Author

Listed:
  • Elisabeth Gassiat
  • Céline Lévy‐Leduc

Abstract

. We consider the estimation of the periods of periodic functions when their shape is unknown and they are corrupted by Gaussian white noise. In the case of a single periodic function, we propose a consistent and asymptotically efficient semiparametric estimator of the period. We then study the case of a sum of two periodic functions of unknown shape with different periods and propose semiparametric estimators of their periods that are consistent and asymptotically Gaussian.

Suggested Citation

  • Elisabeth Gassiat & Céline Lévy‐Leduc, 2006. "Efficient Semiparametric Estimation of the Periods in a Superposition of Periodic Functions with Unknown Shape," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 877-910, November.
  • Handle: RePEc:bla:jtsera:v:27:y:2006:i:6:p:877-910
    DOI: 10.1111/j.1467-9892.2006.00493.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9892.2006.00493.x
    Download Restriction: no

    File URL: https://libkey.io/10.1111/j.1467-9892.2006.00493.x?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. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Oliver Linton & Michael Vogt, 2012. "Nonparametric estimation of a periodic sequence in the presence of a smooth trend," CeMMAP working papers 23/12, Institute for Fiscal Studies.
    2. Michael Vogt & Oliver Linton, 2014. "Nonparametric estimation of a periodic sequence in the presence of a smooth trend," Biometrika, Biometrika Trust, vol. 101(1), pages 121-140.
    3. C. Lévy‐Leduc & E. Moulines & F. Roueff, 2008. "Frequency estimation based on the cumulated Lomb–Scargle periodogram," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 1104-1131, November.

    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. Yang, Lijian & Park, Byeong U. & Xue, Lan & Hardle, Wolfgang, 2006. "Estimation and Testing for Varying Coefficients in Additive Models With Marginal Integration," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1212-1227, September.
    2. Koop, Gary & Dijk, Herman K. Van, 2000. "Testing for integration using evolving trend and seasonals models: A Bayesian approach," Journal of Econometrics, Elsevier, vol. 97(2), pages 261-291, August.
    3. Elizabeth Bucacos, 2008. "Real (effective) exchange rate in Uruguay: a periodic cointegration approach," Monetaria, CEMLA, vol. 0(2), pages 265-289, julio-sep.
    4. Jonathan Aylen & Kevin Albertson & Gina Cavan, 2014. "The impact of weather and climate on tourist demand: the case of Chester Zoo," Climatic Change, Springer, vol. 127(2), pages 183-197, November.
    5. Niels Haldrup & Antonio Montañés & Andreu Sansó, 2004. "Testing for Additive Outliers in Seasonally Integrated Time Series," Economics Working Papers 2004-14, Department of Economics and Business Economics, Aarhus University.
    6. Paulo Rodrigues & Denise Osborn, 1999. "Performance of seasonal unit root tests for monthly data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(8), pages 985-1004.
    7. Beenstock, Michael & Reingewertz, Yaniv & Paldor, Nathan, 2016. "Testing the historic tracking of climate models," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1234-1246.
    8. Łukasz Lenart & Błażej Mazur, 2016. "On Bayesian Inference for Almost Periodic in Mean Autoregressive Models," FindEcon Chapters: Forecasting Financial Markets and Economic Decision-Making, in: Magdalena Osińska (ed.), Statistical Review, vol. 63, 2016, 3, edition 1, volume 63, chapter 1, pages 255-272, University of Lodz.
    9. Yorghos Tripodis & Jeremy Penzer, 2009. "Modelling time series with season-dependent autocorrelation structure," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(7), pages 559-574.
    10. Hamori, Shigeyuki, 2001. "Seasonality and stock returns: some evidence from Japan," Japan and the World Economy, Elsevier, vol. 13(4), pages 463-481, December.
    11. Evren Erdoğan Cosar, 2006. "Seasonal behaviour of the consumer price index of Turkey," Applied Economics Letters, Taylor & Francis Journals, vol. 13(7), pages 449-455.
    12. Man, K. S., 2004. "Linear prediction of temporal aggregates under model misspecification," International Journal of Forecasting, Elsevier, vol. 20(4), pages 659-670.
    13. Georgi N. Boshnakov & Bisher M. Iqelan, 2009. "Generation Of Time Series Models With Given Spectral Properties," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(3), pages 349-368, May.
    14. Cai, Zongwu, 2003. "Trending Time-Varying Coefficient Models With Serially Correlated Errors," SFB 373 Discussion Papers 2003,7, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    15. A. Christian Silva & Ju-Yi Yen, 2010. "Stochastic resonance and the trade arrival rate of stocks," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 461-466.
    16. M. Angeles Carnero & Siem Jan Koopman & Marius Ooms, 2003. "Periodic Heteroskedastic RegARFIMA Models for Daily Electricity Spot Prices," Tinbergen Institute Discussion Papers 03-071/4, Tinbergen Institute.
    17. Artur Silva Lopes, 2006. "Deterministic seasonality in Dickey–Fuller tests: should we care?," Empirical Economics, Springer, vol. 31(1), pages 165-182, March.
    18. Bauer, Dietmar, 2019. "Periodic and seasonal (co-)integration in the state space framework," Economics Letters, Elsevier, vol. 174(C), pages 165-168.
    19. Franses, P.H. & McAleer, M., 1995. "Testing Nested and Non-Nested Periodically Integrated Autoregressive Models," Papers 9510, Tilburg - Center for Economic Research.
    20. Clements, Michael & Smith, Jeremy, 1997. "Forecasting Seasonal Uk Consumption Components," Economic Research Papers 268761, University of Warwick - Department of Economics.

    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:jtsera:v:27:y:2006:i:6:p:877-910. 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: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.