IDEAS home Printed from https://ideas.repec.org/a/oup/biomet/v101y2014i1p121-140..html
   My bibliography  Save this article

Nonparametric estimation of a periodic sequence in the presence of a smooth trend

Author

Listed:
  • Michael Vogt
  • Oliver Linton

Abstract

We investigate a nonparametric regression model including a periodic component, a smooth trend function, and a stochastic error term. We propose a procedure to estimate the unknown period and the function values of the periodic component as well as the nonparametric trend function. The theoretical part of the paper establishes the asymptotic properties of our estimators. In particular, we show that our estimator of the period is consistent. In addition, we derive the convergence rates and the limiting distributions of our estimators of the periodic component and the trend function. The asymptotic results are complemented with a simulation study and an application to global temperature anomaly data.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:101:y:2014:i:1:p:121-140.
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1093/biomet/ast051
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kristensen, Dennis, 2009. "Uniform Convergence Rates Of Kernel Estimators With Heterogeneous Dependent Data," Econometric Theory, Cambridge University Press, vol. 25(5), pages 1433-1445, October.
    2. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, October.
    3. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    4. Atak, Alev & Linton, Oliver & Xiao, Zhijie, 2011. "A semiparametric panel model for unbalanced data with application to climate change in the United Kingdom," Journal of Econometrics, Elsevier, vol. 164(1), pages 92-115, September.
    5. Peter Hall & Ming Li, 2006. "Using the periodogram to estimate period in nonparametric regression," Biometrika, Biometrika Trust, vol. 93(2), pages 411-424, June.
    6. repec:hal:journl:peer-00844810 is not listed on IDEAS
    7. Hirotugu Akaike, 1969. "Fitting autoregressive models for prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 243-247, December.
    8. Robert M. De Jong & James Davidson, 2000. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Econometrica, Econometric Society, vol. 68(2), pages 407-424, March.
    9. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    10. 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.
    11. D'Andrade, Kendall, 1992. "The End of an Era," Business Ethics Quarterly, Cambridge University Press, vol. 2(3), pages 379-389, July.
    12. Peter Hall & Jiying Yin, 2003. "Nonparametric methods for deconvolving multiperiodic functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 869-886, November.
    13. Michael Vogt, 2012. "Nonparametric regression for locally stationary time series," CeMMAP working papers CWP22/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. Marc G. Genton & Peter Hall, 2007. "Statistical inference for evolving periodic functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 643-657, September.
    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. Michael Vogt & Oliver Linton, 2015. "Classification of nonparametric regression functions in heterogeneous panels," CeMMAP working papers 06/15, Institute for Fiscal Studies.
    2. Linton, Oliver & Wu, Jianbin, 2020. "A coupled component DCS-EGARCH model for intraday and overnight volatility," Journal of Econometrics, Elsevier, vol. 217(1), pages 176-201.
    3. Vogt, Michael & Linton, Oliver, 2020. "Multiscale clustering of nonparametric regression curves," Journal of Econometrics, Elsevier, vol. 216(1), pages 305-325.
    4. Peter Malec, 2016. "A Semiparametric Intraday GARCH Model," Cambridge Working Papers in Economics 1633, Faculty of Economics, University of Cambridge.
    5. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2014. "Multivariate variance ratio statistics," CeMMAP working papers CWP29/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Seok Young Hong & Oliver Linton & Hui Jun Zhang, 2014. "Multivariate variance ratio statistics," CeMMAP working papers 29/14, Institute for Fiscal Studies.
    7. Kai Yang & Peihua Qiu, 2022. "A three-step local smoothing approach for estimating the mean and covariance functions of spatio-temporal Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(1), pages 49-68, February.
    8. Koo, B. & La Vecchia, D. & Linton, O., 2019. "Nonparametric Recovery of the Yield Curve Evolution from Cross-Section and Time Series Information," Cambridge Working Papers in Economics 1916, Faculty of Economics, University of Cambridge.
    9. Michael Vogt & Oliver Linton, 2015. "Classification of nonparametric regression functions in heterogeneous panels," CeMMAP working papers CWP06/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Koo, Bonsoo & La Vecchia, Davide & Linton, Oliver, 2021. "Estimation of a nonparametric model for bond prices from cross-section and time series information," Journal of Econometrics, Elsevier, vol. 220(2), pages 562-588.
    11. Liu, Jialuo & Chu, Tingjin & Zhu, Jun & Wang, Haonan, 2021. "Semiparametric method and theory for continuously indexed spatio-temporal processes," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    12. Marina Khismatullina & Michael Vogt, 2022. "Multiscale Comparison of Nonparametric Trend Curves," Papers 2209.10841, arXiv.org.

    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. 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. Chen, Zhihong & Xia, Huizhu, 2020. "Trend instrumental variable regression with an application to the US New Keynesian Phillips Curve," Economic Modelling, Elsevier, vol. 93(C), pages 595-604.
    3. Paulo M. D. C. Parente & Richard J. Smith, 2021. "Quasi‐maximum likelihood and the kernel block bootstrap for nonlinear dynamic models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 377-405, July.
    4. Chen, Qitong & Hong, Yongmiao & Li, Haiqi, 2024. "Time-varying forecast combination for factor-augmented regressions with smooth structural changes," Journal of Econometrics, Elsevier, vol. 240(1).
    5. Hall, Viv B & Thomson, Peter, 2022. "A boosted HP filter for business cycle analysis: evidence from New Zealand’s small open economy," Working Paper Series 9473, Victoria University of Wellington, School of Economics and Finance.
    6. David T. Frazier & Bonsoo Koo, 2020. "Indirect Inference for Locally Stationary Models," Monash Econometrics and Business Statistics Working Papers 30/20, Monash University, Department of Econometrics and Business Statistics.
    7. Ricardo Reis & Vasco Curdia, 2009. "Correlated Disturbances and U.S. Business Cycles," 2009 Meeting Papers 129, Society for Economic Dynamics.
    8. Boubaker, Heni & Cunado, Juncal & Gil-Alana, Luis A. & Gupta, Rangan, 2020. "Global crises and gold as a safe haven: Evidence from over seven and a half centuries of data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    9. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, May.
    10. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2016. "Common Drifting Volatility in Large Bayesian VARs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 375-390, July.
    11. Fondeur, Y. & Karamé, F., 2013. "Can Google data help predict French youth unemployment?," Economic Modelling, Elsevier, vol. 30(C), pages 117-125.
    12. Federico Belotti & Alessandro Casini & Leopoldo Catania & Stefano Grassi & Pierre Perron, 2023. "Simultaneous bandwidths determination for DK-HAC estimators and long-run variance estimation in nonparametric settings," Econometric Reviews, Taylor & Francis Journals, vol. 42(3), pages 281-306, February.
    13. Bernardi Mauro & Della Corte Giuseppe & Proietti Tommaso, 2011. "Extracting the Cyclical Component in Hours Worked," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(3), pages 1-28, May.
    14. repec:zbw:bofitp:2011_035 is not listed on IDEAS
    15. Francis Vitek, 2005. "An Unobserved Components Model of the Monetary Transmission Mechanism in a Small Open Economy," Macroeconomics 0512019, University Library of Munich, Germany, revised 06 Feb 2006.
    16. de Castro, Luciano & Galvao, Antonio F. & Kaplan, David M. & Liu, Xin, 2019. "Smoothed GMM for quantile models," Journal of Econometrics, Elsevier, vol. 213(1), pages 121-144.
    17. Karlsson, Sune, 2013. "Forecasting with Bayesian Vector Autoregression," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 791-897, Elsevier.
    18. Gabauer, David & Gupta, Rangan, 2020. "Spillovers across macroeconomic, financial and real estate uncertainties: A time-varying approach," Structural Change and Economic Dynamics, Elsevier, vol. 52(C), pages 167-173.
    19. J. Isaac Miller, 2010. "Cointegrating regressions with messy regressors and an application to mixed‐frequency series," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(4), pages 255-277, July.
    20. Malin Gardberg & Lorenzo Pozzi, 2022. "Aggregate consumption and wealth in the long run: The impact of financial liberalization," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(1), pages 161-186, January.
    21. David I. Stern & Robert K. Kaufmann, 1997. "Time series properties of global climate variables: detection and attribution of climate change," Working Papers in Ecological Economics 9702, Australian National University, Centre for Resource and Environmental Studies, Ecological Economics Program.

    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:oup:biomet:v:101:y:2014:i:1:p:121-140.. 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: Oxford University Press (email available below). General contact details of provider: https://academic.oup.com/biomet .

    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.