IDEAS home Printed from https://ideas.repec.org/p/bde/wpaper/1230.html
   My bibliography  Save this paper

A model for vast panels of volatilities

Author

Listed:
  • Matteo Luciani

    (Université Libre de Bruxelles)

  • David Veredas

    (Université Libre de Bruxelles)

Abstract

Realized volatilities, when observed over time, share the following stylised facts: comovements, clustering, long-memory, dynamic volatility, skewness and heavy-tails. We propose a dynamic factor model that captures these stylised facts and that can be applied to vast panels of volatilities as it does not suffer from the curse of dimensionality. It is an enhanced version of Bai and Ng (2004) in the following respects: i) we allow for longmemory in both the idiosyncratic and the common components, ii) the common shocks are conditionally heteroskedastic, and iii) the idiosyncratic and common shocks are skewed and heavy-tailed. Estimation of the factors, the idiosyncratic components and the parameters is simple: principal components and low dimension maximum likelihood estimations. A Monte Carlo study shows the usefulness of the approach and an application to 90 daily realized volatilities, pertaining to S&P100, from January 2001 to December 2008, evinces, among others, the following findings: i) All the volatilities have long-memory, more than half in the nonstationary range, that increases during financial turmoils. ii) Tests and criteria point towards one dynamic common factor driving the co-movements. iii) The factor has larger long-memory than the assets volatilities, suggesting that long–memory is a market characteristic. iv) The volatility of the realized volatility is not constant and common to all. v) A forecasting horse race against 8 competing models shows that our model outperforms, in particular in periods of stress.

Suggested Citation

  • Matteo Luciani & David Veredas, 2012. "A model for vast panels of volatilities," Working Papers 1230, Banco de España.
  • Handle: RePEc:bde:wpaper:1230
    as

    Download full text from publisher

    File URL: http://www.bde.es/f/webbde/SES/Secciones/Publicaciones/PublicacionesSeriadas/DocumentosTrabajo/12/Fich/dt1230e.pdf
    File Function: First version, September 2012
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Søren Johansen & Morten Ørregaard Nielsen, 2012. "Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model," Econometrica, Econometric Society, vol. 80(6), pages 2667-2732, November.
    2. 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.
    3. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2005. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 830-840, September.
    4. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    5. Roxana Halbleib & Valerie Voev, 2011. "Forecasting Covariance Matrices: A Mixed Frequency Approach," Working Papers ECARES ECARES 2011-002, ULB -- Universite Libre de Bruxelles.
    6. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1113-1141, December.
    7. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    8. 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.
    9. 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.
    10. Fulvio Corsi & Stefan Mittnik & Christian Pigorsch & Uta Pigorsch, 2008. "The Volatility of Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 46-78.
    11. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    12. Kapetanios, George, 2010. "A Testing Procedure for Determining the Number of Factors in Approximate Factor Models With Large Datasets," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 397-409.
    13. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
    14. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    15. Bai, Jushan & Ng, Serena, 2007. "Determining the Number of Primitive Shocks in Factor Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 52-60, January.
    16. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    17. Kirman Alan & Teyssière Gilles, 2002. "Microeconomic Models for Long Memory in the Volatility of Financial Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 5(4), pages 1-23, January.
    18. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    19. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, July.
    20. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    21. Bårdsen, Gunnar & Lütkepohl, Helmut, 2011. "Forecasting levels of log variables in vector autoregressions," International Journal of Forecasting, Elsevier, vol. 27(4), pages 1108-1115, October.
    22. Matteo Barigozzi & Christian T. Brownlees & Giampiero M. Gallo & David Veredas, 2010. "Disentangling Systematic and Idiosyncratic Risk for Large Panels of Assets," Econometrics Working Papers Archive wp2010_06, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    23. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
    24. Granger, Clive W. J. & Hyung, Namwon, 2004. "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 399-421, June.
    25. Hansen, Peter Reinhard & Lunde, Asger, 2006. "Consistent ranking of volatility models," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 97-121.
    26. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range‐Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, June.
    27. Lucia Alessi & Matteo Barigozzi & Marco Capasso, 2009. "Forecasting Large Datasets with Conditionally Heteroskedastic Dynamic Common Factors," Working Papers ECARES 2009_005, ULB -- Universite Libre de Bruxelles.
    28. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    29. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    30. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    31. Alexei Onatski, 2010. "Determining the Number of Factors from Empirical Distribution of Eigenvalues," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1004-1016, November.
    32. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    33. Johansen, SØren, 2008. "A Representation Theory For A Class Of Vector Autoregressive Models For Fractional Processes," Econometric Theory, Cambridge University Press, vol. 24(3), pages 651-676, June.
    34. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, September.
    35. Tibor F. Liska, 2007. "The Liska model," Society and Economy, Akadémiai Kiadó, Hungary, vol. 29(3), pages 363-381, December.
    36. Cătălin Stărică & Clive Granger, 2005. "Nonstationarities in Stock Returns," The Review of Economics and Statistics, MIT Press, vol. 87(3), pages 503-522, August.
    37. Alessi, Lucia & Barigozzi, Matteo & Capasso, Marco, 2009. "Estimation and forecasting in large datasets with conditionally heteroskedastic dynamic common factors," Working Paper Series 1115, European Central Bank.
    38. Amengual, Dante & Watson, Mark W., 2007. "Consistent Estimation of the Number of Dynamic Factors in a Large N and T Panel," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 91-96, January.
    39. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
    40. Gourieroux, C. & Jasiak, J. & Sufana, R., 2009. "The Wishart Autoregressive process of multivariate stochastic volatility," Journal of Econometrics, Elsevier, vol. 150(2), pages 167-181, June.
    41. Alessi, Lucia & Barigozzi, Matteo & Capasso, Marco, 2010. "Improved penalization for determining the number of factors in approximate factor models," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1806-1813, December.
    42. Hallin, Marc & Liska, Roman, 2007. "Determining the Number of Factors in the General Dynamic Factor Model," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 603-617, June.
    43. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    44. Jushan Bai & Serena Ng, 2006. "Confidence Intervals for Diffusion Index Forecasts and Inference for Factor-Augmented Regressions," Econometrica, Econometric Society, vol. 74(4), pages 1133-1150, July.
    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. Sayantan Bandhu Majumder & Ranjanendra Narayan Nag, 2018. "Shock and Volatility Spillovers Among Equity Sectors of the National Stock Exchange in India," Global Business Review, International Management Institute, vol. 19(1), pages 227-240, February.
    2. Mardi Dungey & Matteo Luciani & David Veredas, 2012. "Ranking Systemically Important Financial Institutions," CAMA Working Papers 2012-47, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    3. Herskovic, Bernard & Kelly, Bryan & Lustig, Hanno & Van Nieuwerburgh, Stijn, 2016. "The common factor in idiosyncratic volatility: Quantitative asset pricing implications," Journal of Financial Economics, Elsevier, vol. 119(2), pages 249-283.
    4. Fady Barsoum, 2013. "The Effects of Monetary Policy Shocks on a Panel of Stock Market Volatilities: A Factor-Augmented Bayesian VAR Approach," Working Paper Series of the Department of Economics, University of Konstanz 2013-15, Department of Economics, University of Konstanz.
    5. Adam Clements & Ayesha Scott & Annastiina Silvennoinen, 2013. "On the Benefits of Equicorrelation for Portfolio Allocation," NCER Working Paper Series 99, National Centre for Econometric Research.
    6. Bernard Herskovic & Bryan Kelly & Hanno Lustig & Stijn Van Nieuwerburgh, 2020. "Firm Volatility in Granular Networks," Journal of Political Economy, University of Chicago Press, vol. 128(11), pages 4097-4162.
    7. Ilze KALNINA & Kokouvi TEWOU, 2015. "Cross-sectional Dependence in Idiosyncratic Volatility," Cahiers de recherche 08-2015, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    8. Barigozzi, Matteo & Brownlees, Christian & Gallo, Giampiero M. & Veredas, David, 2014. "Disentangling systematic and idiosyncratic dynamics in panels of volatility measures," Journal of Econometrics, Elsevier, vol. 182(2), pages 364-384.
    9. Yunus Emre Ergemen, 2016. "Generalized Efficient Inference on Factor Models with Long-Range Dependence," CREATES Research Papers 2016-05, Department of Economics and Business Economics, Aarhus University.
    10. Adam E Clements & Ayesha Scott & Annastiina Silvennoinen, 2012. "Forecasting multivariate volatility in larger dimensions: some practical issues," NCER Working Paper Series 80, National Centre for Econometric Research.
    11. Stijn Van Nieuwerburgh & Hanno Lustig & Bryan Kelly & Bernard Herskovic, 2014. "The Common Factor in Idiosyncratic Volatility," 2014 Meeting Papers 810, Society for Economic Dynamics.
    12. Ezzat, Hassan, 2012. "The Application of GARCH Methods in Modeling Volatility Using Sector Indices from the Egyptian Exchange," MPRA Paper 51584, University Library of Munich, Germany.

    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. Matteo Luciani & David Veredas, "undated". "A simple model for vast panels of volatilities," ULB Institutional Repository 2013/136239, ULB -- Universite Libre de Bruxelles.
    2. Pilar Poncela & Esther Ruiz, 2016. "Small- Versus Big-Data Factor Extraction in Dynamic Factor Models: An Empirical Assessment," Advances in Econometrics, in: Dynamic Factor Models, volume 35, pages 401-434, Emerald Group Publishing Limited.
    3. Matteo Luciani, 2015. "Monetary Policy and the Housing Market: A Structural Factor Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(2), pages 199-218, March.
    4. Matteo Barigozzi & Antonio M. Conti & Matteo Luciani, 2014. "Do Euro Area Countries Respond Asymmetrically to the Common Monetary Policy?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(5), pages 693-714, October.
    5. Catherine Doz & Peter Fuleky, 2019. "Dynamic Factor Models," Working Papers 2019-4, University of Hawaii Economic Research Organization, University of Hawaii at Manoa.
    6. Poncela, Pilar & Ruiz, Esther & Miranda, Karen, 2021. "Factor extraction using Kalman filter and smoothing: This is not just another survey," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1399-1425.
    7. Barigozzi, Matteo & Hallin, Marc, 2017. "Generalized dynamic factor models and volatilities: estimation and forecasting," Journal of Econometrics, Elsevier, vol. 201(2), pages 307-321.
    8. Jörg Breitung & In Choi, 2013. "Factor models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 11, pages 249-265, Edward Elgar Publishing.
      • In Choi & Jorg Breitung, 2011. "Factor models," Working Papers 1121, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy), revised Dec 2011.
    9. Barigozzi, Matteo & Lippi, Marco & Luciani, Matteo, 2021. "Large-dimensional Dynamic Factor Models: Estimation of Impulse–Response Functions with I(1) cointegrated factors," Journal of Econometrics, Elsevier, vol. 221(2), pages 455-482.
    10. Heaton, Chris & Solo, Victor, 2012. "Estimation of high-dimensional linear factor models with grouped variables," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 348-367.
    11. Mario Forni & Luca Gambetti & Luca Sala, 2014. "No News in Business Cycles," Economic Journal, Royal Economic Society, vol. 124(581), pages 1168-1191, December.
    12. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    13. Matteo Barigozzi & Marco Lippi & Matteo Luciani, 2016. "Non-Stationary Dynamic Factor Models for Large Datasets," Finance and Economics Discussion Series 2016-024, Board of Governors of the Federal Reserve System (U.S.).
    14. Ergemen, Yunus Emre & Rodríguez-Caballero, C. Vladimir, 2023. "Estimation of a dynamic multi-level factor model with possible long-range dependence," International Journal of Forecasting, Elsevier, vol. 39(1), pages 405-430.
    15. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    16. Forni, Mario & Cavicchioli, Maddalena & Lippi, Marco & Zaffaroni, Paolo, 2016. "Eigenvalue Ratio Estimators for the Number of Common Factors," CEPR Discussion Papers 11440, C.E.P.R. Discussion Papers.
    17. Matteo Barigozzi & Marco Lippi & Matteo Luciani, 2014. "Dynamic Factor Models, Cointegration and Error Correction Mechanisms," Working Papers ECARES ECARES 2014-14, ULB -- Universite Libre de Bruxelles.
    18. Francisco Corona & Pilar Poncela & Esther Ruiz, 2017. "Determining the number of factors after stationary univariate transformations," Empirical Economics, Springer, vol. 53(1), pages 351-372, August.
    19. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    20. Forni, Mario & Hallin, Marc & Lippi, Marco & Zaffaroni, Paolo, 2015. "Dynamic factor models with infinite-dimensional factor spaces: One-sided representations," Journal of Econometrics, Elsevier, vol. 185(2), pages 359-371.

    More about this item

    Keywords

    Realized volatilities; vast dimensions; factor models; long–memory; forecasting;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G01 - Financial Economics - - General - - - Financial Crises

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:bde:wpaper:1230. 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: Ángel Rodríguez. Electronic Dissemination of Information Unit. Research Department. Banco de España (email available below). General contact details of provider: https://edirc.repec.org/data/bdegves.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.