IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb649/sfb649dp2011-003.html
   My bibliography  Save this paper

Mean volatility regressions

Author

Listed:
  • Lin, Lu
  • Li, Feng
  • Zhu, Lixing
  • Härdle, Wolfgang Karl

Abstract

Motivated by increment process modeling for two correlated random and non-random systems from a discrete-time asset pricing with both risk free asset and risky security, we propose a class of semiparametric regressions for a combination of a non-random and a random system. Unlike classical regressions, mean regression functions in the new model contain variance components and the model variables are related to latent variables, for which certain economic interpretation can be made. The motivating example explains why the GARCH-M of which the mean function contains a variance component cannot cover the newly proposed models. Further, we show that statistical inference for the increment process cannot be simply dealt with by a two-step procedure working separately on the two involved systems although the increment process is a weighted sum of the two systems. We further investigate the asymptotic behaviors of estimation by using sophisticated nonparametric smoothing. Monte Carlo simulations are conducted to examine finite-sample performance, and a real dataset published in Almanac of China's Finance and Banking (2004 and 2005) is analyzed for illustration about the increment process of wealth in financial market of China from 2003 to 2004.

Suggested Citation

  • Lin, Lu & Li, Feng & Zhu, Lixing & Härdle, Wolfgang Karl, 2010. "Mean volatility regressions," SFB 649 Discussion Papers 2011-003, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
  • Handle: RePEc:zbw:sfb649:sfb649dp2011-003
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/56687/1/642765502.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    2. Kim, Tae Yoon & Cox, Dennis D., 1996. "Uniform strong consistency of kernel density estimators under dependence," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 179-185, February.
    3. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    4. Bradley, Richard C. & Bryc, Wlodzimierz, 1985. "Multilinear forms and measures of dependence between random variables," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 335-367, June.
    Full references (including those not matched with items on IDEAS)

    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. Chen, Bin & Song, Zhaogang, 2013. "Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach," Journal of Econometrics, Elsevier, vol. 173(1), pages 83-107.
    2. repec:hum:wpaper:sfb649dp2011-003 is not listed on IDEAS
    3. Christensen, Kim & Oomen, Roel & Podolskij, Mark, 2010. "Realised quantile-based estimation of the integrated variance," Journal of Econometrics, Elsevier, vol. 159(1), pages 74-98, November.
    4. Peter Feldhütter & Christian Heyerdahl-Larsen & Philipp Illeditsch, 2018. "Risk Premia and Volatilities in a Nonlinear Term Structure Model [Quadratic term structure models: theory and evidence]," Review of Finance, European Finance Association, vol. 22(1), pages 337-380.
    5. Turan Bali, 2007. "Modeling the dynamics of interest rate volatility with skewed fat-tailed distributions," Annals of Operations Research, Springer, vol. 151(1), pages 151-178, April.
    6. Griffin, J.E. & Steel, M.F.J., 2006. "Inference with non-Gaussian Ornstein-Uhlenbeck processes for stochastic volatility," Journal of Econometrics, Elsevier, vol. 134(2), pages 605-644, October.
    7. Corradi, Valentina & Distaso, Walter & Fernandes, Marcelo, 2012. "International market links and volatility transmission," Journal of Econometrics, Elsevier, vol. 170(1), pages 117-141.
    8. Diep Duong & Norman R. Swanson, 2011. "Volatility in Discrete and Continuous Time Models: A Survey with New Evidence on Large and Small Jumps," Departmental Working Papers 201117, Rutgers University, Department of Economics.
    9. Hillebrand, Eric & Schnabl, Gunther & Ulu, Yasemin, 2009. "Japanese foreign exchange intervention and the yen-to-dollar exchange rate: A simultaneous equations approach using realized volatility," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 19(3), pages 490-505, July.
    10. Christophe Chorro & Florian Ielpo & Benoît Sévi, 2017. "The contribution of jumps to forecasting the density of returns," Post-Print halshs-01442618, HAL.
    11. Christos Floros & Konstantinos Gkillas & Christoforos Konstantatos & Athanasios Tsagkanos, 2020. "Realized Measures to Explain Volatility Changes over Time," JRFM, MDPI, vol. 13(6), pages 1-19, June.
    12. Katerina Papagiannouli, 2022. "A Lepskiĭ-type stopping rule for the covariance estimation of multi-dimensional Lévy processes," Statistical Inference for Stochastic Processes, Springer, vol. 25(3), pages 505-535, October.
    13. repec:kap:iaecre:v:14:y:2008:i:1:p:112-124 is not listed on IDEAS
    14. Podolskij, Mark & Vetter, Mathias, 2009. "Bipower-type estimation in a noisy diffusion setting," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2803-2831, September.
    15. Cavit Pakel & Neil Shephard & Kevin Sheppard, 2009. "Nuisance parameters, composite likelihoods and a panel of GARCH models," OFRC Working Papers Series 2009fe03, Oxford Financial Research Centre.
    16. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2017. "Decoupling the short- and long-term behavior of stochastic volatility," CREATES Research Papers 2017-26, Department of Economics and Business Economics, Aarhus University.
    17. Elsayed, Ahmed H. & Asutay, Mehmet & ElAlaoui, Abdelkader O. & Bin Jusoh, Hashim, 2024. "Volatility spillover across spot and futures markets: Evidence from dual financial system," Research in International Business and Finance, Elsevier, vol. 71(C).
    18. Wang, Fangfang, 2014. "Optimal design of Fourier estimator in the presence of microstructure noise," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 708-722.
    19. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
    20. Patrick Saart & Jiti Gao & Nam Hyun Kim, 2014. "Semiparametric methods in nonlinear time series analysis: a selective review," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 141-169, March.
    21. Jonathan J. Reeves & Xuan Xie, 2014. "Forecasting stock return volatility at the quarterly frequency: an evaluation of time series approaches," Applied Financial Economics, Taylor & Francis Journals, vol. 24(5), pages 347-356, March.
    22. Alexander Schnurr, 2015. "An Ordinal Pattern Approach to Detect and to Model Leverage Effects and Dependence Structures Between Financial Time Series," Papers 1502.07321, arXiv.org.

    More about this item

    Keywords

    non-random systems; random systems; semiparametric regression; variance built-in mean;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • J01 - Labor and Demographic Economics - - General - - - Labor Economics: General
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials

    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:zbw:sfb649:sfb649dp2011-003. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sohubde.html .

    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.