IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v101y2017i3d10.1007_s10182-017-0288-1.html
   My bibliography  Save this article

Fourier methods for analyzing piecewise constant volatilities

Author

Listed:
  • Max Wornowizki

    (TU Dortmund University)

  • Roland Fried

    (TU Dortmund University)

  • Simos G. Meintanis

    (National and Kapodistrian University of Athens
    North-West University)

Abstract

We develop procedures for testing whether a sequence of independent random variables has constant variance. If this is fulfilled, the modulus of a Fourier-type transformation of the volatility process is identically equal to one. Our approach takes advantage of this property considering a canonical estimator for the modulus under the assumption of piecewise identically distributed zero mean observations. Using blockwise variance estimation, we introduce several test statistics resulting from different weight functions. All of them are given by simple explicit formulae. We prove the consistency of the corresponding tests and compare them to alternative procedures on extensive Monte Carlo experiments. According to the results, our proposals offer fairly high power, particularly in the case of multiple structural breaks. They also allow for an adequate estimation of the change point positions. We apply our procedure to gold mining data and also briefly discuss how it can be modified to test for the stationarity of other distributional parameters.

Suggested Citation

  • Max Wornowizki & Roland Fried & Simos G. Meintanis, 2017. "Fourier methods for analyzing piecewise constant volatilities," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(3), pages 289-308, July.
    • Handle: RePEc:spr:alstar:v:101:y:2017:i:3:d:10.1007_s10182-017-0288-1
    DOI: 10.1007/s10182-017-0288-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10182-017-0288-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10182-017-0288-1?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. Bruno Feunou & Roméo Tédongap, 2012. "A Stochastic Volatility Model With Conditional Skewness," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(4), pages 576-591, July.
    2. Jiménez-Gamero, M.D. & Alba-Fernández, V. & Muñoz-García, J. & Chalco-Cano, Y., 2009. "Goodness-of-fit tests based on empirical characteristic functions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3957-3971, October.
    3. Ross, Gordon J., 2013. "Modelling financial volatility in the presence of abrupt changes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(2), pages 350-360.
    4. Fried, Roland, 2012. "On the online estimation of local constant volatilities," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3080-3090.
    5. Cornelis J. Potgieter & Marc G. Genton, 2013. "Characteristic Function-based Semiparametric Inference for Skew-symmetric Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 471-490, September.
    6. Chris Brooks, 2005. "Autoregressive Conditional Kurtosis," Journal of Financial Econometrics, Oxford University Press, vol. 3(3), pages 399-421.
    7. Zdeněk Hlávka & Marie Hušková & Claudia Kirch & Simos Meintanis, 2012. "Monitoring changes in the error distribution of autoregressive models based on Fourier methods," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(4), pages 605-634, December.
    8. D. A. Hsu, 1977. "Tests for Variance Shift at an Unknown Time Point," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 26(3), pages 279-284, November.
    9. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(4), pages 465-487, December.
    10. Dominik Wied & Matthias Arnold & Nicolai Bissantz & Daniel Ziggel, 2012. "A new fluctuation test for constant variances with applications to finance," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1111-1127, November.
    11. Tenreiro, Carlos, 2009. "On the choice of the smoothing parameter for the BHEP goodness-of-fit test," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1038-1053, February.
    12. Jandhyala, Venkata K. & Fotopoulos, Stergios B. & Hawkins, Douglas M., 2002. "Detection and estimation of abrupt changes in the variability of a process," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 1-19, July.
    13. David S. Matteson & Nicholas A. James, 2014. "A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 334-345, March.
    14. Davies, Laurie & Höhenrieder, Christian & Krämer, Walter, 2012. "Recursive computation of piecewise constant volatilities," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3623-3631.
    15. Epps, T. W., 1999. "Limiting behavior of the ICF test for normality under Gram-Charlier alternatives," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 175-184, April.
    16. Juan Carlos Pardo-Fernández & María Dolores Jiménez-Gamero & Anouar El Ghouch, 2015. "A Non-parametric ANOVA-type Test for Regression Curves Based on Characteristic Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 197-213, March.
    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. Ieva Axt & Roland Fried, 2020. "On variance estimation under shifts in the mean," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 417-457, September.

    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. Meintanis, Simos G. & Ushakov, Nikolai G., 2016. "Nonparametric probability weighted empirical characteristic function and applications," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 52-61.
    2. Lee, Sangyeol & Meintanis, Simos G. & Pretorius, Charl, 2022. "Monitoring procedures for strict stationarity based on the multivariate characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. J. S. Allison & M. Hušková & S. G. Meintanis, 2018. "Testing the adequacy of semiparametric transformation models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 70-94, March.
    4. Alex Huang, 2013. "Value at risk estimation by quantile regression and kernel estimator," Review of Quantitative Finance and Accounting, Springer, vol. 41(2), pages 225-251, August.
    5. Sujay K Mukhoti, "undated". "Dynamic Feedback Effect And Skewness In Non-Stationary Stochastic Volatility Model With Leverage," Working papers 145, Indian Institute of Management Kozhikode.
    6. Michael Messer, 2022. "Bivariate change point detection: Joint detection of changes in expectation and variance," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 886-916, June.
    7. Tenreiro, Carlos, 2011. "An affine invariant multiple test procedure for assessing multivariate normality," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 1980-1992, May.
    8. Lim, Kian Guan & Chen, Ying & Yap, Nelson K.L., 2019. "Intraday information from S&P 500 Index futures options," Journal of Financial Markets, Elsevier, vol. 42(C), pages 29-55.
    9. Liu, Xiaochun & Luger, Richard, 2015. "Unfolded GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 58(C), pages 186-217.
    10. Zdeněk Hlávka & Marie Hušková & Simos G. Meintanis, 2020. "Change-point methods for multivariate time-series: paired vectorial observations," Statistical Papers, Springer, vol. 61(4), pages 1351-1383, August.
    11. Yang (Greg) Hou & Mark Holmes, 2020. "Do higher order moments of return distribution provide better decisions in minimum-variance hedging? Evidence from US stock index futures," Australian Journal of Management, Australian School of Business, vol. 45(2), pages 240-265, May.
    12. Benjamin Beckers & Helmut Herwartz & Moritz Seidel, 2017. "Risk forecasting in (T)GARCH models with uncorrelated dependent innovations," Quantitative Finance, Taylor & Francis Journals, vol. 17(1), pages 121-137, January.
    13. Hou, Yang (Greg) & Li, Steven, 2020. "Volatility and skewness spillover between stock index and stock index futures markets during a crash period: New evidence from China," International Review of Economics & Finance, Elsevier, vol. 66(C), pages 166-188.
    14. Al Rahahleh, Naseem & Bhatti, M. Ishaq, 2017. "Co-movement measure of information transmission on international equity markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 119-131.
    15. Bruno Feunou & Mohammad R. Jahan-Parvar & Roméo Tédongap, 2016. "Which parametric model for conditional skewness?," The European Journal of Finance, Taylor & Francis Journals, vol. 22(13), pages 1237-1271, October.
    16. Lhuissier, Stéphane, 2022. "Financial conditions and macroeconomic downside risks in the euro area," European Economic Review, Elsevier, vol. 143(C).
    17. Stefan Albert & Michael Messer & Julia Schiemann & Jochen Roeper & Gaby Schneider, 2017. "Multi-Scale Detection of Variance Changes in Renewal Processes in the Presence of Rate Change Points," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 1028-1052, November.
    18. Florian Pein & Hannes Sieling & Axel Munk, 2017. "Heterogeneous change point inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1207-1227, September.
    19. Chen, Bin & Hong, Yongmiao, 2014. "A unified approach to validating univariate and multivariate conditional distribution models in time series," Journal of Econometrics, Elsevier, vol. 178(P1), pages 22-44.
    20. Heni Boubaker & Nadia Sghaier, 2015. "On the Dynamic Dependence between US and other Developed Stock Markets: An Extreme-value Time-varying Copula Approach," Bankers, Markets & Investors, ESKA Publishing, issue 136-137, pages 80-93, May-June.

    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:spr:alstar:v:101:y:2017:i:3:d:10.1007_s10182-017-0288-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.