IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v27y2008i1-3p254-267.html
   My bibliography  Save this article

Refined Inference on Long Memory in Realized Volatility

Author

Listed:
  • Offer Lieberman
  • Peter Phillips

Abstract

There is an emerging consensus in empirical finance that realized volatility series typically display long range dependence with a memory parameter (d) around 0.4 (Andersen et al., 2001; Martens et al., 2004). The present article provides some illustrative analysis of how long memory may arise from the accumulative process underlying realized volatility. The article also uses results in Lieberman and Phillips (2004, 2005) to refine statistical inference about d by higher order theory. Standard asymptotic theory has an O(n-1/2) error rate for error rejection probabilities, and the theory used here refines the approximation to an error rate of o(n-1/2). The new formula is independent of unknown parameters, is simple to calculate and user-friendly. The method is applied to test whether the reported long memory parameter estimates of Andersen et al. (2001) and Martens et al. (2004) differ significantly from the lower boundary (d = 0.5) of nonstationary long memory, and generally confirms earlier findings.

Suggested Citation

  • Offer Lieberman & Peter Phillips, 2008. "Refined Inference on Long Memory in Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 254-267.
  • Handle: RePEc:taf:emetrv:v:27:y:2008:i:1-3:p:254-267
    DOI: 10.1080/07474930701873374
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/07474930701873374
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/07474930701873374?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    2. Deo, Rohit & Hurvich, Clifford & Lu, Yi, 2006. "Forecasting realized volatility using a long-memory stochastic volatility model: estimation, prediction and seasonal adjustment," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 29-58.
    3. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation for Research in Economics, Yale University.
    4. Andersen, Torben G & Bollerslev, Tim, 1997. "Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," Journal of Finance, American Finance Association, vol. 52(3), pages 975-1005, July.
    5. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    6. Lieberman, Offer & Phillips, Peter C.B., 2004. "Expansions For The Distribution Of The Maximum Likelihood Estimator Of The Fractional Difference Parameter," Econometric Theory, Cambridge University Press, vol. 20(3), pages 464-484, June.
    7. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 351-416.
    8. Martin Martens & Dick van Dijk & Michiel de Pooter, 2004. "Modeling and Forecasting S&P 500 Volatility: Long Memory, Structural Breaks and Nonlinearity," Tinbergen Institute Discussion Papers 04-067/4, Tinbergen Institute.
    9. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    10. 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.
    11. Offer Lieberman & Peter C. B. Phillips, 2005. "Expansions for approximate maximum likelihood estimators of the fractional difference parameter," Econometrics Journal, Royal Economic Society, vol. 8(3), pages 367-379, December.
    12. Zhang, Lan & Mykland, Per A. & Aït-Sahalia, Yacine, 2011. "Edgeworth expansions for realized volatility and related estimators," Journal of Econometrics, Elsevier, vol. 160(1), pages 190-203, January.
    13. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    14. Pong, Shiuyan & Shackleton, Mark B. & Taylor, Stephen J. & Xu, Xinzhong, 2004. "Forecasting currency volatility: A comparison of implied volatilities and AR(FI)MA models," Journal of Banking & Finance, Elsevier, vol. 28(10), pages 2541-2563, October.
    15. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    16. Federico M. Bandi & Benoit Perron, 2006. "Long Memory and the Relation Between Implied and Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 4(4), pages 636-670.
    17. Clifford M. Hurvich & Rohit Deo & Julia Brodsky, 1998. "The mean squared error of Geweke and Porter‐Hudak's estimator of the memory parameter of a long‐memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 19-46, January.
    18. K Abadir & W Distaso & L Giraitis, "undated". "Local Whittle estimation, fully extended for nonstationarity," Discussion Papers 05/16, Department of Economics, University of York.
    19. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    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. Lieberman, Offer & Phillips, Peter C.B., 2008. "A complete asymptotic series for the autocovariance function of a long memory process," Journal of Econometrics, Elsevier, vol. 147(1), pages 99-103, November.
    2. Luis F. Espinoza-Audelo & Maricruz Olazabal-Lugo & Fabio Blanco-Mesa & Ernesto León-Castro & Victor Alfaro-Garcia, 2020. "Bonferroni Probabilistic Ordered Weighted Averaging Operators Applied to Agricultural Commodities’ Price Analysis," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    3. Bauwens, Luc & Chevillon, Guillaume & Laurent, Sébastien, 2023. "We modeled long memory with just one lag!," Journal of Econometrics, Elsevier, vol. 236(1).
    4. Zhang, Lan & Mykland, Per A. & Aït-Sahalia, Yacine, 2011. "Edgeworth expansions for realized volatility and related estimators," Journal of Econometrics, Elsevier, vol. 160(1), pages 190-203, January.
    5. McAleer, Michael & Medeiros, Marcelo C., 2008. "A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries," Journal of Econometrics, Elsevier, vol. 147(1), pages 104-119, November.
    6. Matteo Luciani & David Veredas, 2012. "A model for vast panels of volatilities," Working Papers 1230, Banco de España.
    7. Rossi, Eduardo & Santucci de Magistris, Paolo, 2013. "Long memory and tail dependence in trading volume and volatility," Journal of Empirical Finance, Elsevier, vol. 22(C), pages 94-112.
    8. Chevillon, Guillaume & Hecq , Alain & Laurent, Sébastien, 2015. "Long Memory Through Marginalization of Large Systems and Hidden Cross-Section Dependence," ESSEC Working Papers WP1507, ESSEC Research Center, ESSEC Business School.
    9. Zhanglong Wang & Kent Wang & Zheyao Pan, 2015. "Conditional equity risk premia and realized variance jump risk," Australian Journal of Management, Australian School of Business, vol. 40(2), pages 295-317, May.
    10. Grassi, Stefano & Santucci de Magistris, Paolo, 2015. "It's all about volatility of volatility: Evidence from a two-factor stochastic volatility model," Journal of Empirical Finance, Elsevier, vol. 30(C), pages 62-78.
    11. Liudas Giraitis & Donatas Surgailis & Andrius Škarnulis, 2015. "Integrated ARCH, FIGARCH and AR Models: Origins of Long Memory," Working Papers 766, Queen Mary University of London, School of Economics and Finance.
    12. J. Arteche, 2012. "Semiparametric Inference in Correlated Long Memory Signal Plus Noise Models," Econometric Reviews, Taylor & Francis Journals, vol. 31(4), pages 440-474.
    13. Liudas Giraitis & Donatas Surgailis & Andrius Škarnulis, 2015. "Integrated ARCH, FIGARCH and AR Models: Origins of Long Memory," Working Papers 766, Queen Mary University of London, School of Economics and Finance.
    14. Matteo Luciani & David Veredas, "undated". "A simple model for vast panels of volatilities," ULB Institutional Repository 2013/136239, ULB -- Universite Libre de Bruxelles.
    15. Stefano Grassi & Nima Nonejad & Paolo Santucci De Magistris, 2017. "Forecasting With the Standardized Self‐Perturbed Kalman Filter," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(2), pages 318-341, March.
    16. Fulvio Corsi & Roberto Renò, 2012. "Discrete-Time Volatility Forecasting With Persistent Leverage Effect and the Link With Continuous-Time Volatility Modeling," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 368-380, January.
    17. Tian, Fengping & Yang, Ke & Chen, Langnan, 2017. "Realized volatility forecasting of agricultural commodity futures using the HAR model with time-varying sparsity," International Journal of Forecasting, Elsevier, vol. 33(1), pages 132-152.
    18. Matei, Marius, 2011. "Non-Linear Volatility Modeling of Economic and Financial Time Series Using High Frequency Data," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 116-141, June.
    19. Ding, Yi & Kambouroudis, Dimos & McMillan, David G., 2021. "Forecasting realised volatility: Does the LASSO approach outperform HAR?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 74(C).
    20. Alexandra Chronopoulou & Frederi Viens, 2012. "Estimation and pricing under long-memory stochastic volatility," Annals of Finance, Springer, vol. 8(2), pages 379-403, 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. Bollerslev, Tim & Kretschmer, Uta & Pigorsch, Christian & Tauchen, George, 2009. "A discrete-time model for daily S & P500 returns and realized variations: Jumps and leverage effects," Journal of Econometrics, Elsevier, vol. 150(2), pages 151-166, June.
    2. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
    3. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2006. "Predicting volatility: getting the most out of return data sampled at different frequencies," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 59-95.
    4. Torben G. Andersen & Luca Benzoni, 2008. "Realized volatility," Working Paper Series WP-08-14, Federal Reserve Bank of Chicago.
    5. Matei, Marius, 2011. "Non-Linear Volatility Modeling of Economic and Financial Time Series Using High Frequency Data," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 116-141, June.
    6. Andersen, Torben G. & Bollerslev, Tim & Huang, Xin, 2011. "A reduced form framework for modeling volatility of speculative prices based on realized variation measures," Journal of Econometrics, Elsevier, vol. 160(1), pages 176-189, January.
    7. Michael McAleer & Marcelo Medeiros, 2008. "Realized Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 10-45.
    8. Andersen, Torben G. & Bollerslev, Tim & Meddahi, Nour, 2011. "Realized volatility forecasting and market microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 220-234, January.
    9. Bertrand B. Maillet & Jean-Philippe R. M�decin, 2010. "Extreme Volatilities, Financial Crises and L-moment Estimations of Tail-indexes," Working Papers 2010_10, Department of Economics, University of Venice "Ca' Foscari".
    10. McAleer, Michael & Medeiros, Marcelo C., 2008. "A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries," Journal of Econometrics, Elsevier, vol. 147(1), pages 104-119, November.
    11. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2003. "Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump Components in Measuring, Modeling, and Forecasting Asset Return Volatility," PIER Working Paper Archive 03-025, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Sep 2003.
    12. Patton, Andrew J. & Sheppard, Kevin, 2009. "Optimal combinations of realised volatility estimators," International Journal of Forecasting, Elsevier, vol. 25(2), pages 218-238.
    13. Maheu, John M. & McCurdy, Thomas H., 2011. "Do high-frequency measures of volatility improve forecasts of return distributions?," Journal of Econometrics, Elsevier, vol. 160(1), pages 69-76, January.
    14. Marcelo C. Carvalho & Marco Aurélio S. Freire & Marcelo Cunha Medeiros & Leonardo R. Souza, 2006. "Modeling and Forecasting the Volatility of Brazilian Asset Returns: a Realized Variance Approach," Brazilian Review of Finance, Brazilian Society of Finance, vol. 4(1), pages 55-77.
    15. 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.
    16. Raggi, Davide & Bordignon, Silvano, 2012. "Long memory and nonlinearities in realized volatility: A Markov switching approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3730-3742.
    17. Julien Chevallier & Benoît Sévi, 2011. "On the realized volatility of the ECX CO 2 emissions 2008 futures contract: distribution, dynamics and forecasting," Annals of Finance, Springer, vol. 7(1), pages 1-29, February.
    18. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    19. Aït-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2011. "Ultra high frequency volatility estimation with dependent microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 160-175, January.
    20. Ole E. Barndorff-Nielsen & Neil Shephard, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," OFRC Working Papers Series 2005fe08, Oxford Financial Research Centre.

    More about this item

    Keywords

    Edgeworth expansion; Long memory; Realized volatility;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    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:emetrv:v:27:y:2008:i:1-3:p:254-267. 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: the person in charge (email available below). General contact details of provider: http://www.tandfonline.com/LECR20 .

    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.