IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v76y2006i18p2007-2016.html
   My bibliography  Save this article

Nonparametric estimation of volatility models with serially dependent innovations

Author

Listed:
  • Dahl, Christian M.
  • Levine, Michael

Abstract

We are interested in modelling the time series process yt=[sigma](xt)[epsilon]t, where [epsilon]t=[phi]0[epsilon]t-1+vt. This model is of interest as it provides a plausible linkage between risk and expected return of financial assets. Further, the model can serve as a vehicle for testing the martingale difference sequence hypothesis, which is typically uncritically adopted in financial time series models. When xt has a fixed design, we provide a novel nonparametric estimator of the variance function based on the difference approach and establish its limiting properties. When xt is strictly stationary on a strongly mixing base (hereby allowing for ARCH effects) the nonparametric variance function estimator by Fan and Yao [1998. Efficient estimation of conditional variance functions in stochastic regression. Biometrika 85, 645-660] can be applied and seems very promising. We propose a semiparametric estimator of [phi]0 that is -consistent, adaptive, and asymptotic normally distributed under very general conditions on xt.

Suggested Citation

  • Dahl, Christian M. & Levine, Michael, 2006. "Nonparametric estimation of volatility models with serially dependent innovations," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 2007-2016, December.
  • Handle: RePEc:eee:stapro:v:76:y:2006:i:18:p:2007-2016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(06)00187-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Andrews, Donald W K, 1987. "Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers [On Unification of the Asymptotic Theory of Nonlinear Econometric Models]," Econometrica, Econometric Society, vol. 55(6), pages 1465-1471, November.
    2. Bierens,Herman J., 2005. "Introduction to the Mathematical and Statistical Foundations of Econometrics," Cambridge Books, Cambridge University Press, number 9780521834315, November.
    3. Karim M. Abadir & Jan R. Magnus, 2002. "Notation in econometrics: a proposal for a standard," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 76-90, June.
    4. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    5. 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.
    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. Brandan K. Beare, 2008. "Unit Root Testing with Unstable Volatility," Economics Series Working Papers 2008-WO6, University of Oxford, Department of Economics.
    2. Dalla, Violetta & Giraitis, Liudas & Robinson, Peter M., 2020. "Asymptotic theory for time series with changing mean and variance," Journal of Econometrics, Elsevier, vol. 219(2), pages 281-313.
    3. Brendan K. Beare, 2018. "Unit Root Testing with Unstable Volatility," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 816-835, November.
    4. Dahl Christian M & Iglesias Emma, 2011. "Modeling the Volatility-Return Trade-Off When Volatility May Be Nonstationary," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-32, February.

    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. Gregory Connor & Matthias Hagmann & Oliver Linton, 2007. "Efficient Estimation of a Semiparametric Characteristic- Based Factor Model of Security Returns," Swiss Finance Institute Research Paper Series 07-26, Swiss Finance Institute.
    2. Francesco Bravo & Ba M. Chu & David T. Jacho-Chávez, 2017. "Semiparametric estimation of moment condition models with weakly dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 108-136, January.
    3. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    4. Arturas Juodis, 2013. "Cointegration Testing in Panel VAR Models Under Partial Identification and Spatial Dependence," UvA-Econometrics Working Papers 13-08, Universiteit van Amsterdam, Dept. of Econometrics.
    5. Sandy Fréret & Denis Maguain, 2017. "The effects of agglomeration on tax competition: evidence from a two-regime spatial panel model on French data," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 24(6), pages 1100-1140, December.
    6. Hoderlein, Stefan & White, Halbert, 2012. "Nonparametric identification in nonseparable panel data models with generalized fixed effects," Journal of Econometrics, Elsevier, vol. 168(2), pages 300-314.
    7. Jing Lv & Chaohui Guo, 2017. "Efficient parameter estimation via modified Cholesky decomposition for quantile regression with longitudinal data," Computational Statistics, Springer, vol. 32(3), pages 947-975, September.
    8. 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.
    9. Whang, Yoon-Jae & Linton, Oliver, 1999. "The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series," Journal of Econometrics, Elsevier, vol. 91(1), pages 1-42, July.
    10. Yanchun Jin, 2016. "Nonparametric tests for the effect of treatment on conditional variance," KIER Working Papers 948, Kyoto University, Institute of Economic Research.
    11. Holger Dette & Kay Pilz, 2009. "On the estimation of a monotone conditional variance in nonparametric regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 111-141, March.
    12. M. Hashem Pesaran & Yongcheol Shin, 2002. "Long-Run Structural Modelling," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 49-87.
    13. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    14. Dingshi Tian & Zongwu Cai & Ying Fang, 2018. "Econometric Modeling of Risk Measures: A Selective Review of the Recent Literature," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201807, University of Kansas, Department of Economics, revised Oct 2018.
    15. Miller, Steve & Startz, Richard, 2019. "Feasible generalized least squares using support vector regression," Economics Letters, Elsevier, vol. 175(C), pages 28-31.
    16. Xingcai Zhou & Dehan Kong & Matthew Stephen Pietrosanu & Linglong Kong & Rohana J. Karunamuni, 2024. "Empirical likelihood M‐estimation for the varying‐coefficient model with functional response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 1357-1387, September.
    17. Sokbae Lee & Myung Hwan Seo & Youngki Shin, 2017. "Correction," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 883-883, April.
    18. Undral Byambadalai & Tatsushi Oka & Shota Yasui, 2024. "Estimating Distributional Treatment Effects in Randomized Experiments: Machine Learning for Variance Reduction," Papers 2407.16037, arXiv.org.
    19. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    20. Alexandre Belloni & Victor Chernozhukov & Ivan Fernandez-Val & Christian Hansen, 2013. "Program evaluation with high-dimensional data," CeMMAP working papers CWP77/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    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:eee:stapro:v:76:y:2006:i:18:p:2007-2016. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.