IDEAS home Printed from https://ideas.repec.org/a/jae/japmet/v14y1999i3p309-18.html
   My bibliography  Save this article

Testing for a Unit Root in the Volatility of Asset Returns

Author

Listed:
  • Wright, Jonathan H

Abstract

It is now well established that the volatility of asset returns is time varying and highly persistent. One leading model that is used to represent these features of the data is the stochastic volatility model. The researcher may test for non-stationarity of the volatility process by testing for a unit root in the log-squared time series. This strategy for inference has many advantages, but is not followed in practice because these unit root tests are known to have very poor size properties. In this paper I show that new tests that are robust to negative MA roots allow a reliable test for a unit root in the volatility process to be conducted. In applying these tests to exchange rate and stock returns, strong rejections of non-stationarity in volatility are obtained.

Suggested Citation

  • Wright, Jonathan H, 1999. "Testing for a Unit Root in the Volatility of Asset Returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(3), pages 309-318, May-June.
    • Handle: RePEc:jae:japmet:v:14:y:1999:i:3:p:309-18
    as

    Download full text from publisher

    File URL: http://qed.econ.queensu.ca:80/jae/1999-v14.3/
    File Function: Supporting data files and programs
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400.
    2. Andersen, Torben G & Sorensen, Bent E, 1996. "GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 328-352, July.
    3. Pierre Perron & Serena Ng, 1996. "Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(3), pages 435-463.
    4. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    5. Pantula, Sastry G, 1991. "Asymptotic Distributions of Unit-Root Tests When the Process Is Nearly Stationary," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 63-71, January.
    6. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
    7. Shephard, Neil, 1993. "Fitting Nonlinear Time-Series Models with Applications to Stochastic Variance Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 135-152, Suppl. De.
    8. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    9. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    10. Dacorogna, Michael M. & Muller, Ulrich A. & Nagler, Robert J. & Olsen, Richard B. & Pictet, Olivier V., 1993. "A geographical model for the daily and weekly seasonal volatility in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 12(4), pages 413-438, August.
    11. 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.
    12. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    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. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-059, New York University, Leonard N. Stern School of Business-.
    2. Athanasia Gavala & Nikolay Gospodinov & Deming Jiang, 2006. "Forecasting volatility," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(6), pages 381-400.
    3. Luis Gil-Alana, 2003. "Stochastic behavior of nominal exchange rates," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 31(2), pages 159-173, June.
    4. Kevin B. Grier & Aaron D. Smallwood, 2007. "Uncertainty and Export Performance: Evidence from 18 Countries," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(4), pages 965-979, June.
    5. Hansen, Peter R. & Lunde, Asger, 2014. "Estimating The Persistence And The Autocorrelation Function Of A Time Series That Is Measured With Error," Econometric Theory, Cambridge University Press, vol. 30(1), pages 60-93, February.
    6. Benth, Fred Espen & Paraschiv, Florentina, 2018. "A space-time random field model for electricity forward prices," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 203-216.
    7. Yong Li & Jun Yu, 2010. "A New Bayesian Unit Root Test in Stochastic Volatility Models," Working Papers 21-2010, Singapore Management University, School of Economics, revised Oct 2010.
    8. Patton, Andrew J., 2011. "Data-based ranking of realised volatility estimators," Journal of Econometrics, Elsevier, vol. 161(2), pages 284-303, April.
    9. Yong Li & Jun Yu, 2019. "An Improved Bayesian Unit Root Test in Stochastic Volatility Models," Annals of Economics and Finance, Society for AEF, vol. 20(1), pages 103-122, May.

    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. Yu, Jun & Yang, Zhenlin & Zhang, Xibin, 2006. "A class of nonlinear stochastic volatility models and its implications for pricing currency options," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2218-2231, December.
    2. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    3. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    4. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
    5. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    6. Pezzo, Rosanna & Uberti, Mariacristina, 2006. "Approaches to forecasting volatility: Models and their performances for emerging equity markets," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 556-565.
    7. Jun Yu, 2007. "Automated Likelihood Based Inference for Stochastic Volatility Models," Working Papers 01-2007, Singapore Management University, Sim Kee Boon Institute for Financial Economics.
    8. Hautsch, Nikolaus & Ou, Yangguoyi, 2008. "Discrete-time stochastic volatility models and MCMC-based statistical inference," SFB 649 Discussion Papers 2008-063, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    9. Alexander Tsyplakov, 2010. "Revealing the arcane: an introduction to the art of stochastic volatility models (in Russian)," Quantile, Quantile, issue 8, pages 69-122, July.
    10. Andersen, Torben G & Sorensen, Bent E, 1996. "GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 328-352, July.
    11. Font, Begoña, 1998. "Modelización de series temporales financieras. Una recopilación," DES - Documentos de Trabajo. Estadística y Econometría. DS 3664, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Andersen, Torben G. & Chung, Hyung-Jin & Sorensen, Bent E., 1999. "Efficient method of moments estimation of a stochastic volatility model: A Monte Carlo study," Journal of Econometrics, Elsevier, vol. 91(1), pages 61-87, July.
    13. Joan del Castillo & Juan-Pablo Ortega, 2011. "Hedging of time discrete auto-regressive stochastic volatility options," Papers 1110.6322, arXiv.org.
    14. Tsyplakov, Alexander, 2010. "Revealing the arcane: an introduction to the art of stochastic volatility models," MPRA Paper 25511, University Library of Munich, Germany.
    15. Ben Tims & Ronald Mahieu, 2006. "A Range-Based Multivariate Stochastic Volatility Model for Exchange Rates," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 409-424.
    16. Jun Yu & Renate Meyer, 2006. "Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 361-384.
    17. N. Balakrishna & Bovas Abraham & Ranjini Sivakumar, 2006. "Gamma stochastic volatility models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(3), pages 153-171.
    18. Vo, Minh, 2011. "Oil and stock market volatility: A multivariate stochastic volatility perspective," Energy Economics, Elsevier, vol. 33(5), pages 956-965, September.
    19. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    20. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, September.

    More about this item

    Lists

    This item is featured on the following reading lists, Wikipedia, or ReplicationWiki pages:
    1. Testing for a unit root in the volatility of asset returns (Journal of Applied Econometrics 1999) in ReplicationWiki

    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:jae:japmet:v:14:y:1999:i:3:p:309-18. 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: Wiley-Blackwell Digital Licensing or Christopher F. Baum (email available below). General contact details of provider: http://www.interscience.wiley.com/jpages/0883-7252/ .

    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.