IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v192y2016i1p19-39.html
   My bibliography  Save this article

Bayesian semiparametric modeling of realized covariance matrices

Author

Listed:
  • Jin, Xin
  • Maheu, John M.

Abstract

This paper introduces several new Bayesian nonparametric models suitable for capturing the unknown conditional distribution of realized covariance (RCOV) matrices. Existing dynamic Wishart models are extended to countably infinite mixture models of Wishart and inverse-Wishart distributions. In addition to mixture models with constant weights we propose models with time-varying weights to capture time dependence in the unknown distribution. Each of our models can be combined with returns to provide a coherent joint model of returns and RCOV. The extensive forecast results show the new models provide very significant improvements in density forecasts for RCOV and returns and competitive point forecasts of RCOV.

Suggested Citation

  • Jin, Xin & Maheu, John M., 2016. "Bayesian semiparametric modeling of realized covariance matrices," Journal of Econometrics, Elsevier, vol. 192(1), pages 19-39.
    • Handle: RePEc:eee:econom:v:192:y:2016:i:1:p:19-39
    DOI: 10.1016/j.jeconom.2015.11.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407615002729
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2015.11.001?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. repec:hal:journl:peer-00815564 is not listed on IDEAS
    2. Markus Jochmann, 2015. "Modeling U.S. Inflation Dynamics: A Bayesian Nonparametric Approach," Econometric Reviews, Taylor & Francis Journals, vol. 34(5), pages 537-558, May.
    3. Fulvio Corsi & Stefano Peluso & Francesco Audrino, 2015. "Missing in Asynchronicity: A Kalman‐em Approach for Multivariate Realized Covariance Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(3), pages 377-397, April.
    4. Shu-Ping Shi & Yong Song, 2012. "Identifying Speculative Bubbles with an Infinite Hidden Markov Model," Working Paper series 26_12, Rimini Centre for Economic Analysis.
    5. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    6. Nikolaus Hautsch & Lada M. Kyj & Roel C. A. Oomen, 2012. "A blocking and regularization approach to high‐dimensional realized covariance estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(4), pages 625-645, June.
    7. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, May.
    8. Jensen, Mark J. & Maheu, John M., 2013. "Bayesian semiparametric multivariate GARCH modeling," Journal of Econometrics, Elsevier, vol. 176(1), pages 3-17.
    9. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Journal of Econometrics, Elsevier, vol. 162(2), pages 149-169, June.
    10. Maria Kalli & Jim Griffin, 2015. "Flexible Modeling of Dependence in Volatility Processes," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 102-113, January.
    11. Xin Jin & John M. Maheu, 2013. "Modeling Realized Covariances and Returns," Journal of Financial Econometrics, Oxford University Press, vol. 11(2), pages 335-369, March.
    12. Teh, Yee Whye & Jordan, Michael I. & Beal, Matthew J. & Blei, David M., 2006. "Hierarchical Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1566-1581, December.
    13. Roxana Chiriac & Valeri Voev, 2011. "Modelling and forecasting multivariate realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(6), pages 922-947, September.
    14. Keisuke Hirano, 2002. "Semiparametric Bayesian Inference in Autoregressive Panel Data Models," Econometrica, Econometric Society, vol. 70(2), pages 781-799, March.
    15. Luc Bauwens & Manuela Braione & Giuseppe Storti, 2016. "Forecasting Comparison of Long Term Component Dynamic Models for Realized Covariance Matrices," Annals of Economics and Statistics, GENES, issue 123-124, pages 103-134.
    16. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2014. "Beta-product dependent Pitman–Yor processes for Bayesian inference," Journal of Econometrics, Elsevier, vol. 180(1), pages 49-72.
    17. Diaa Noureldin & Neil Shephard & Kevin Sheppard, 2012. "Multivariate high‐frequency‐based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 907-933, September.
    18. 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.
    19. Conley, Timothy G. & Hansen, Christian B. & McCulloch, Robert E. & Rossi, Peter E., 2008. "A semi-parametric Bayesian approach to the instrumental variable problem," Journal of Econometrics, Elsevier, vol. 144(1), pages 276-305, May.
    20. K. Triantafyllopoulos, 2012. "Multi‐variate stochastic volatility modelling using Wishart autoregressive processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(1), pages 48-60, January.
    21. Golosnoy, Vasyl & Gribisch, Bastian & Liesenfeld, Roman, 2012. "The conditional autoregressive Wishart model for multivariate stock market volatility," Journal of Econometrics, Elsevier, vol. 167(1), pages 211-223.
    22. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    23. 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.
    24. Audrone Virbickaite & M. Concepción Ausín & Pedro Galeano, 2015. "Bayesian Inference Methods For Univariate And Multivariate Garch Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 29(1), pages 76-96, February.
    25. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
    26. DUFAYS, Arnaud, 2012. "Infinite-state Markov-switching for dynamic volatility and correlation models," LIDAM Discussion Papers CORE 2012043, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    27. Yong Song, 2014. "Modelling Regime Switching And Structural Breaks With An Infinite Hidden Markov Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(5), pages 825-842, August.
    28. 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.
    29. Kevin Sheppard & Wen Xu, 2014. "Factor High-Frequency Based Volatility (HEAVY) Models," Economics Series Working Papers 710, University of Oxford, Department of Economics.
    30. Burda, Martin & Harding, Matthew & Hausman, Jerry, 2008. "A Bayesian mixed logit-probit model for multinomial choice," Journal of Econometrics, Elsevier, vol. 147(2), pages 232-246, December.
    31. Bauer, Gregory H. & Vorkink, Keith, 2011. "Forecasting multivariate realized stock market volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 93-101, January.
    32. Chib, Siddhartha & Greenberg, Edward, 2010. "Additive cubic spline regression with Dirichlet process mixture errors," Journal of Econometrics, Elsevier, vol. 156(2), pages 322-336, June.
    33. Peter Reinhard Hansen & Asger Lunde & Valeri Voev, 2014. "Realized Beta Garch: A Multivariate Garch Model With Realized Measures Of Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(5), pages 774-799, August.
    34. Rodríguez, Abel & Dunson, David B & Gelfand, Alan E, 2008. "The Nested Dirichlet Process," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1131-1154.
    35. Philipov, Alexander & Glickman, Mark E., 2006. "Multivariate Stochastic Volatility via Wishart Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 313-328, July.
    36. Griffin, J.E. & Steel, M.F.J., 2011. "Stick-breaking autoregressive processes," Journal of Econometrics, Elsevier, vol. 162(2), pages 383-396, June.
    37. Alexander Philipov & Mark Glickman, 2006. "Factor Multivariate Stochastic Volatility via Wishart Processes," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 311-334.
    38. Pawel Janus & André Lucas & Anne Opschoor & Dick J.C. van Dijk, 2014. "New HEAVY Models for Fat-Tailed Returns and Realized Covariance Kernels," Tinbergen Institute Discussion Papers 14-073/IV, Tinbergen Institute, revised 19 Aug 2015.
    39. Matteo Bonato & Massimiliano Caporin & Angelo Ranaldo, 2009. "Forecasting realized (co)variances with a block structure Wishart autoregressive model," Working Papers 2009-03, Swiss National Bank.
    40. Mark J. Jensen & John M. Maheu, 2018. "Risk, Return and Volatility Feedback: A Bayesian Nonparametric Analysis," JRFM, MDPI, vol. 11(3), pages 1-29, September.
    41. Delatola, E.-I. & Griffin, J.E., 2013. "A Bayesian semiparametric model for volatility with a leverage effect," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 97-110.
    42. Griffin, J.E. & Steel, M.F.J., 2006. "Order-Based Dependent Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 179-194, March.
    43. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
    44. Gregory Bauer & Keith Vorkink, 2007. "Multivariate Realized Stock Market Volatility," Staff Working Papers 07-20, Bank of Canada.
    45. Asai, Manabu & McAleer, Michael, 2009. "The structure of dynamic correlations in multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 150(2), pages 182-192, June.
    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. Hautsch, Nikolaus & Voigt, Stefan, 2019. "Large-scale portfolio allocation under transaction costs and model uncertainty," Journal of Econometrics, Elsevier, vol. 212(1), pages 221-240.
    2. Fisher, Mark & Jensen, Mark J., 2019. "Bayesian inference and prediction of a multiple-change-point panel model with nonparametric priors," Journal of Econometrics, Elsevier, vol. 210(1), pages 187-202.
    3. Shirota, Shinichiro & Omori, Yasuhiro & F. Lopes, Hedibert. & Piao, Haixiang, 2017. "Cholesky realized stochastic volatility model," Econometrics and Statistics, Elsevier, vol. 3(C), pages 34-59.
    4. Luc Bauwens & Jean-François Carpantier & Arnaud Dufays, 2017. "Autoregressive Moving Average Infinite Hidden Markov-Switching Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 162-182, April.
    5. Yaojie Zhang & Yu Wei & Li Liu, 2019. "Improving forecasting performance of realized covariance with extensions of HAR-RCOV model: statistical significance and economic value," Quantitative Finance, Taylor & Francis Journals, vol. 19(9), pages 1425-1438, September.
    6. Xin Jin & Jia Liu & Qiao Yang, 2021. "Does the Choice of Realized Covariance Measures Empirically Matter? A Bayesian Density Prediction Approach," Econometrics, MDPI, vol. 9(4), pages 1-22, December.
    7. Yuta yamauchi & Yasuhiro Omori, 2019. "Multivariate Stochastic Volatility Model with Realized Volatilities and Pairwise Realized Correlations," CIRJE F-Series CIRJE-F-1117, CIRJE, Faculty of Economics, University of Tokyo.
    8. Li, Chenxing, 2022. "A multivariate GARCH model with an infinite hidden Markov mixture," MPRA Paper 112792, University Library of Munich, Germany.
    9. Xin Jin & John M. Maheu & Qiao Yang, 2019. "Bayesian parametric and semiparametric factor models for large realized covariance matrices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(5), pages 641-660, August.
    10. Chenxing Li & John M. Maheu & Qiao Yang, 2024. "An infinite hidden Markov model with stochastic volatility," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(6), pages 2187-2211, September.
    11. Martin, Gael M. & Frazier, David T. & Maneesoonthorn, Worapree & Loaiza-Maya, Rubén & Huber, Florian & Koop, Gary & Maheu, John & Nibbering, Didier & Panagiotelis, Anastasios, 2024. "Bayesian forecasting in economics and finance: A modern review," International Journal of Forecasting, Elsevier, vol. 40(2), pages 811-839.
    12. Yuta Yamauchi & Yasuhiro Omori, 2018. "Multivariate Stochastic Volatility Model with Realized Volatilities and Pairwise Realized Correlations," Papers 1809.09928, arXiv.org, revised Mar 2019.
    13. Gael M. Martin & David T. Frazier & Ruben Loaiza-Maya & Florian Huber & Gary Koop & John Maheu & Didier Nibbering & Anastasios Panagiotelis, 2023. "Bayesian Forecasting in the 21st Century: A Modern Review," Monash Econometrics and Business Statistics Working Papers 1/23, Monash University, Department of Econometrics and Business Statistics.
    14. Jin, Xin & Maheu, John M. & Yang, Qiao, 2022. "Infinite Markov pooling of predictive distributions," Journal of Econometrics, Elsevier, vol. 228(2), pages 302-321.
    15. Andre Lucas & Anne Opschoor & Luca Rossini, 2021. "Tail Heterogeneity for Dynamic Covariance Matrices: the F-Riesz Distribution," Tinbergen Institute Discussion Papers 21-010/III, Tinbergen Institute, revised 11 Jul 2023.
    16. Jan Patrick Hartkopf, 2023. "Composite forecasting of vast-dimensional realized covariance matrices using factor state-space models," Empirical Economics, Springer, vol. 64(1), pages 393-436, January.
    17. Yuta Yamauchi & Yasuhiro Omori, 2016. "Multivariate Stochastic Volatility Model with Realized Volatilities and Pairwise Realized Correlations ," CIRJE F-Series CIRJE-F-1029, CIRJE, Faculty of Economics, University of Tokyo.
    18. Opschoor, Anne & Lucas, André, 2023. "Time-varying variance and skewness in realized volatility measures," International Journal of Forecasting, Elsevier, vol. 39(2), pages 827-840.
    19. I. G. Ukpong & K. G. Balcombe & I. M. Fraser & F. J. Areal, 2019. "Preferences for Mitigation of the Negative Impacts of the Oil and Gas Industry in the Niger Delta Region of Nigeria," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 74(2), pages 811-843, October.
    20. McCausland, William & Miller, Shirley & Pelletier, Denis, 2021. "Multivariate stochastic volatility using the HESSIAN method," Econometrics and Statistics, Elsevier, vol. 17(C), pages 76-94.
    21. Jim Griffin & Maria Kalli & Mark Steel, 2018. "Discussion of “Nonparametric Bayesian Inference in Applications”: Bayesian nonparametric methods in econometrics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 207-218, June.

    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. 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.
    2. Xin Jin & John M. Maheu & Qiao Yang, 2019. "Bayesian parametric and semiparametric factor models for large realized covariance matrices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(5), pages 641-660, August.
    3. Gribisch, Bastian & Hartkopf, Jan Patrick, 2023. "Modeling realized covariance measures with heterogeneous liquidity: A generalized matrix-variate Wishart state-space model," Journal of Econometrics, Elsevier, vol. 235(1), pages 43-64.
    4. Asai, Manabu & McAleer, Michael, 2015. "Forecasting co-volatilities via factor models with asymmetry and long memory in realized covariance," Journal of Econometrics, Elsevier, vol. 189(2), pages 251-262.
    5. Gribisch, Bastian & Hartkopf, Jan Patrick & Liesenfeld, Roman, 2020. "Factor state–space models for high-dimensional realized covariance matrices of asset returns," Journal of Empirical Finance, Elsevier, vol. 55(C), pages 1-20.
    6. Ishihara, Tsunehiro & Omori, Yasuhiro & Asai, Manabu, 2016. "Matrix exponential stochastic volatility with cross leverage," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 331-350.
    7. Jan Patrick Hartkopf, 2023. "Composite forecasting of vast-dimensional realized covariance matrices using factor state-space models," Empirical Economics, Springer, vol. 64(1), pages 393-436, January.
    8. Fengler, Matthias & Okhrin, Ostap, 2012. "Realized Copula," Economics Working Paper Series 1214, University of St. Gallen, School of Economics and Political Science.
    9. BAUWENS, Luc & BRAIONE, Manuela & STORTI, Giuseppe, 2016. "Multiplicative Conditional Correlation Models for Realized Covariance Matrices," LIDAM Discussion Papers CORE 2016041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Roxana Halbleib & Valeri Voev, 2011. "Forecasting Covariance Matrices: A Mixed Frequency Approach," CREATES Research Papers 2011-03, Department of Economics and Business Economics, Aarhus University.
    11. repec:hum:wpaper:sfb649dp2012-034 is not listed on IDEAS
    12. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Fengler, Matthias R. & Okhrin, Ostap, 2016. "Managing risk with a realized copula parameter," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 131-152.
    14. Andrea BUCCI, 2017. "Forecasting Realized Volatility A Review," Journal of Advanced Studies in Finance, ASERS Publishing, vol. 8(2), pages 94-138.
    15. Bastian Gribisch, 2018. "A latent dynamic factor approach to forecasting multivariate stock market volatility," Empirical Economics, Springer, vol. 55(2), pages 621-651, September.
    16. Boudt, Kris & Laurent, Sébastien & Lunde, Asger & Quaedvlieg, Rogier & Sauri, Orimar, 2017. "Positive semidefinite integrated covariance estimation, factorizations and asynchronicity," Journal of Econometrics, Elsevier, vol. 196(2), pages 347-367.
    17. Gribisch, Bastian, 2013. "A latent dynamic factor approach to forecasting multivariate stock market volatility," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79823, Verein für Socialpolitik / German Economic Association.
    18. Shirota, Shinichiro & Omori, Yasuhiro & F. Lopes, Hedibert. & Piao, Haixiang, 2017. "Cholesky realized stochastic volatility model," Econometrics and Statistics, Elsevier, vol. 3(C), pages 34-59.
    19. Hartkopf, Jan Patrick & Reh, Laura, 2023. "Challenging golden standards in EWMA smoothing parameter calibration based on realized covariance measures," Finance Research Letters, Elsevier, vol. 56(C).
    20. Jiayuan Zhou & Feiyu Jiang & Ke Zhu & Wai Keung Li, 2019. "Time series models for realized covariance matrices based on the matrix-F distribution," Papers 1903.12077, arXiv.org, revised Jul 2020.
    21. Yaojie Zhang & Yu Wei & Li Liu, 2019. "Improving forecasting performance of realized covariance with extensions of HAR-RCOV model: statistical significance and economic value," Quantitative Finance, Taylor & Francis Journals, vol. 19(9), pages 1425-1438, September.

    More about this item

    Keywords

    Multi-period density forecasts; Inverse-Wishart distribution; Beam sampling; Hierarchical Dirichlet process; Infinite hidden Markov model;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • 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
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    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:eee:econom:v:192:y:2016:i:1:p:19-39. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.