IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v24y2012i3p699-714.html
   My bibliography  Save this article

Spline confidence bands for variance functions in nonparametric time series regressive models

Author

Listed:
  • Yujiao Yang
  • Yuhang Xu
  • Qiongxia Song

Abstract

For nonparametric time series regression, we propose to apply polynomial splines to squared residuals to develop the variance function estimation. Furthermore, we obtain and use simultaneous confidence bands to detect certain parametric forms for entire variance curves. The proposed method is extremely fast. Asymptotic results are established under the assumption that observations are from a strictly stationary $\alpha$-mixing process. Simulations and a financial data set application are provided to illustrate the performance of the proposed method numerically.

Suggested Citation

  • Yujiao Yang & Yuhang Xu & Qiongxia Song, 2012. "Spline confidence bands for variance functions in nonparametric time series regressive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 699-714.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:3:p:699-714
    DOI: 10.1080/10485252.2012.693925
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485252.2012.693925
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485252.2012.693925?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
    ---><---

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

    References listed on IDEAS

    as
    1. Li Wang & Lijian Yang, 2010. "Simultaneous confidence bands for time-series prediction function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(8), pages 999-1018.
    2. Hardle, W. & Tsybakov, A., 1997. "Local polynomial estimators of the volatility function in nonparametric autoregression," Journal of Econometrics, Elsevier, vol. 81(1), pages 223-242, November.
    3. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    4. Francesco Audrino & Peter Bühlmann, 2009. "Splines for financial volatility," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 655-670, June.
    5. Qiongxia Song & Lijian Yang, 2009. "Spline confidence bands for variance functions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(5), pages 589-609.
    6. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    7. Jianhua Z. Huang & Lijian Yang, 2004. "Identification of non‐linear additive autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 463-477, May.
    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. Shao, Zhen & Gao, Fei & Yang, Shan-Lin & Yu, Ben-gong, 2015. "A new semiparametric and EEMD based framework for mid-term electricity demand forecasting in China: Hidden characteristic extraction and probability density prediction," Renewable and Sustainable Energy Reviews, Elsevier, vol. 52(C), pages 876-889.

    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. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    2. Biqing Cai & Dag Tjøstheim, 2015. "Nonparametric Regression Estimation for Multivariate Null Recurrent Processes," Econometrics, MDPI, vol. 3(2), pages 1-24, April.
    3. Comte, F. & Rozenholc, Y., 2002. "Adaptive estimation of mean and volatility functions in (auto-)regressive models," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 111-145, January.
    4. Chen, Gongmeng & Choi, Yoon K. & Zhou, Yong, 2005. "Nonparametric estimation of structural change points in volatility models for time series," Journal of Econometrics, Elsevier, vol. 126(1), pages 79-114, May.
    5. Joseph Ngatchou-Wandji & Marwa Ltaifa & Didier Alain Njamen Njomen & Jia Shen, 2022. "Nonparametric Estimation of the Density Function of the Distribution of the Noise in CHARN Models," Mathematics, MDPI, vol. 10(4), pages 1-20, February.
    6. Matthieu Garcin & Clément Goulet, 2015. "Non-parameteric news impact curve: a variational approach," Documents de travail du Centre d'Economie de la Sorbonne 15086rr, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Feb 2017.
    7. Gloria González-Rivera & Tae-Hwy Lee, 2007. "Nonlinear Time Series in Financial Forecasting," Working Papers 200803, University of California at Riverside, Department of Economics, revised Feb 2008.
    8. Panagiotis Avramidis, 2016. "Adaptive likelihood estimator of conditional variance function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 132-151, March.
    9. Franke, Jurgen & Neumann, Michael H. & Stockis, Jean-Pierre, 2004. "Bootstrapping nonparametric estimators of the volatility function," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 189-218.
    10. Yujiao Yang & Qiongxia Song, 2014. "Jump detection in time series nonparametric regression models: a polynomial spline approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 325-344, April.
    11. Martins-Filho, Carlos & Yao, Feng & Torero, Maximo, 2018. "Nonparametric Estimation Of Conditional Value-At-Risk And Expected Shortfall Based On Extreme Value Theory," Econometric Theory, Cambridge University Press, vol. 34(1), pages 23-67, February.
    12. Yanchun Jin, 2016. "Nonparametric tests for the effect of treatment on conditional variance," KIER Working Papers 948, Kyoto University, Institute of Economic Research.
    13. Mittnik, Stefan & Robinzonov, Nikolay & Spindler, Martin, 2015. "Stock market volatility: Identifying major drivers and the nature of their impact," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 1-14.
    14. Nicoleta Serban, 2008. "Estimating and clustering curves in the presence of heteroscedastic errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(7), pages 553-571.
    15. Heather L. R. Tierney, 2019. "Forecasting with the Nonparametric Exclusion-from-Core Inflation Persistence Model Using Real-Time Data," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 25(1), pages 39-63, February.
    16. Jianqing Fan, 2004. "A selective overview of nonparametric methods in financial econometrics," Papers math/0411034, arXiv.org.
    17. Linton, Oliver & Mammen, Enno, 2003. "Estimating semiparametric ARCH (8) models by kernel smoothing methods," LSE Research Online Documents on Economics 2187, London School of Economics and Political Science, LSE Library.
    18. Tierney, Heather L.R., 2011. "Real-time data revisions and the PCE measure of inflation," Economic Modelling, Elsevier, vol. 28(4), pages 1763-1773, July.
    19. Lijian Yang & Wolfgang Hardle & Jens Nielsen, 1999. "Nonparametric Autoregression with Multiplicative Volatility and Additive mean," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(5), pages 579-604, September.
    20. Scholz, Achim & Neumeyer, Natalie & Munk, Axel, 2004. "Nonparametric Analysis of Covariance : the Case of Inhomogeneous and Heteroscedastic Noise," Technical Reports 2004,28, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.

    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:taf:gnstxx:v:24:y:2012:i:3:p:699-714. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    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.