IDEAS home Printed from https://ideas.repec.org/a/eee/empfin/v75y2024ics0927539823001305.html
   My bibliography  Save this article

An adaptive long memory conditional correlation model

Author

Listed:
  • Dark, Jonathan

Abstract

We propose a conditional correlation model with long memory dependence and smooth structural change. Previous literature has considered correlation and covariance models with structural change or long memory, but this is the first paper to jointly model both features. The correlation matrix is decomposed into long and short run components. Short run correlations converge hypergeometrically towards a slow moving long run correlation matrix that evolves according to one or more flexible Fourier forms. The model is applied to two data sets: a US equity portfolio; and a US equity, bond, gold and oil portfolio. Model fit and out of sample forecasts over 1 to 60 day horizons support the proposed approach.

Suggested Citation

  • Dark, Jonathan, 2024. "An adaptive long memory conditional correlation model," Journal of Empirical Finance, Elsevier, vol. 75(C).
    • Handle: RePEc:eee:empfin:v:75:y:2024:i:c:s0927539823001305
    DOI: 10.1016/j.jempfin.2023.101463
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0927539823001305
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jempfin.2023.101463?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. Annastiina Silvennoinen & Timo Teräsvirta, 2009. "Modeling Multivariate Autoregressive Conditional Heteroskedasticity with the Double Smooth Transition Conditional Correlation GARCH Model," Journal of Financial Econometrics, Oxford University Press, vol. 7(4), pages 373-411, Fall.
    2. Robert F. Engle & Jose Gonzalo Rangel, 2008. "The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes," The Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1187-1222, May.
    3. Campbell, Rachel & Huisman, Ronald & Koedijk, Kees, 2001. "Optimal portfolio selection in a Value-at-Risk framework," Journal of Banking & Finance, Elsevier, vol. 25(9), pages 1789-1804, September.
    4. 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.
    5. José Rangel & Robert Engle, 2012. "The Factor–Spline–GARCH Model for High and Low Frequency Correlations," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 109-124.
    6. Koopman, Siem Jan & Jungbacker, Borus & Hol, Eugenie, 2005. "Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 445-475, June.
    7. Audrino, Francesco & Corsi, Fulvio, 2010. "Modeling tick-by-tick realized correlations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2372-2382, November.
    8. Haldrup, Niels & Nielsen, Frank S. & Nielsen, Morten Ørregaard, 2010. "A vector autoregressive model for electricity prices subject to long memory and regime switching," Energy Economics, Elsevier, vol. 32(5), pages 1044-1058, September.
    9. Hafner, Christian M. & Linton, Oliver, 2010. "Efficient estimation of a multivariate multiplicative volatility model," Journal of Econometrics, Elsevier, vol. 159(1), pages 55-73, November.
    10. Janus, Paweł & Koopman, Siem Jan & Lucas, André, 2014. "Long memory dynamics for multivariate dependence under heavy tails," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 187-206.
    11. Manabu Asai, 2013. "Heterogeneous Asymmetric Dynamic Conditional Correlation Model with Stock Return and Range," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(5), pages 469-480, August.
    12. 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.
    13. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    14. Banerjee, Anindya & Urga, Giovanni, 2005. "Modelling structural breaks, long memory and stock market volatility: an overview," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 1-34.
    15. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    16. Pelletier, Denis, 2006. "Regime switching for dynamic correlations," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 445-473.
    17. Andreas Noack Jensen & Morten Ørregaard Nielsen, 2014. "A Fast Fractional Difference Algorithm," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 428-436, August.
    18. Luc Bauwens & Christian M. Hafner & Diane Pierret, 2013. "Multivariate Volatility Modeling Of Electricity Futures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 743-761, August.
    19. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    20. Enders Walter & Jones Paul, 2016. "Grain prices, oil prices, and multiple smooth breaks in a VAR," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(4), pages 399-419, September.
    21. Perron, Pierre & Qu, Zhongjun, 2010. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 275-290.
    22. Qu, Zhongjun, 2011. "A Test Against Spurious Long Memory," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 423-438.
    23. Pan, Zhiyuan & Wang, Yudong & Yang, Li, 2014. "Hedging crude oil using refined product: A regime switching asymmetric DCC approach," Energy Economics, Elsevier, vol. 46(C), pages 472-484.
    24. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    25. Baillie, Richard T. & Morana, Claudio, 2009. "Modelling long memory and structural breaks in conditional variances: An adaptive FIGARCH approach," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1577-1592, August.
    26. A. Ronald Gallant, 1984. "The Fourier Flexible Form," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 66(2), pages 204-208.
    27. Robert F. Engle & Eric Ghysels & Bumjean Sohn, 2013. "Stock Market Volatility and Macroeconomic Fundamentals," The Review of Economics and Statistics, MIT Press, vol. 95(3), pages 776-797, July.
    28. 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.
    29. Haldrup Niels & Nielsen Morten Ø., 2006. "Directional Congestion and Regime Switching in a Long Memory Model for Electricity Prices," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(3), pages 1-24, September.
    30. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    31. Blasques, F. & Gorgi, P. & Koopman, S.J., 2019. "Accelerating score-driven time series models," Journal of Econometrics, Elsevier, vol. 212(2), pages 359-376.
    32. Ohanissian, Arek & Russell, Jeffrey R. & Tsay, Ruey S., 2008. "True or Spurious Long Memory? A New Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 161-175, April.
    33. Baillie, Richard T. & Morana, Claudio, 2012. "Adaptive ARFIMA models with applications to inflation," Economic Modelling, Elsevier, vol. 29(6), pages 2451-2459.
    34. 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.
    35. Dark, Jonathan, 2015. "Futures hedging with Markov switching vector error correction FIEGARCH and FIAPARCH," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 269-285.
    36. Bauer, Gregory H. & Vorkink, Keith, 2011. "Forecasting multivariate realized stock market volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 93-101, January.
    37. Hafner, Christian M. & Preminger, Arie, 2009. "On asymptotic theory for multivariate GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2044-2054, October.
    38. 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.
    39. Colacito, Riccardo & Engle, Robert F. & Ghysels, Eric, 2011. "A component model for dynamic correlations," Journal of Econometrics, Elsevier, vol. 164(1), pages 45-59, September.
    40. Chung, Ching-Fan & Baillie, Richard T, 1993. "Small Sample Bias in Conditional Sum-of-Squares Estimators of Fractionally Integrated ARMA Models," Empirical Economics, Springer, vol. 18(4), pages 791-806.
    41. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    42. Davidson, James, 2004. "Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 16-29, January.
    43. Harvey, Andrew & Palumbo, Dario, 2023. "Score-driven models for realized volatility," Journal of Econometrics, Elsevier, vol. 237(2).
    44. repec:hal:journl:peer-00732539 is not listed on IDEAS
    45. Peter Reinhard Hansen & Asger Lunde, 2005. "A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data," Journal of Financial Econometrics, Oxford University Press, vol. 3(4), pages 525-554.
    46. Chen, Rongda & Xu, Jianjun, 2019. "Forecasting volatility and correlation between oil and gold prices using a novel multivariate GAS model," Energy Economics, Elsevier, vol. 78(C), pages 379-391.
    47. František Čech & Jozef Baruník, 2017. "On the Modelling and Forecasting of Multivariate Realized Volatility: Generalized Heterogeneous Autoregressive (GHAR) Model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(2), pages 181-206, March.
    48. Monica Billio & Massimiliano Caporin & Michele Gobbo, 2006. "Flexible Dynamic Conditional Correlation multivariate GARCH models for asset allocation," Applied Financial Economics Letters, Taylor and Francis Journals, vol. 2(2), pages 123-130, March.
    49. Cheryl J. Flynn & Clifford M. Hurvich & Jeffrey S. Simonoff, 2013. "Efficiency for Regularization Parameter Selection in Penalized Likelihood Estimation of Misspecified Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1031-1043, September.
    Full references (including those not matched with items on IDEAS)

    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. Dark, Jonathan, 2018. "Multivariate models with long memory dependence in conditional correlation and volatility," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 162-180.
    2. Kunal Saha & Vinodh Madhavan & Chandrashekhar G. R. & David McMillan, 2020. "Pitfalls in long memory research," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1733280-173, January.
    3. Dark, Jonathan, 2015. "Futures hedging with Markov switching vector error correction FIEGARCH and FIAPARCH," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 269-285.
    4. 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.
    5. 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).
    6. Fengler, Matthias R. & Okhrin, Ostap, 2016. "Managing risk with a realized copula parameter," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 131-152.
    7. Rodríguez, Gabriel, 2017. "Modeling Latin-American stock and Forex markets volatility: Empirical application of a model with random level shifts and genuine long memory," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 393-420.
    8. 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).
    9. João F. Caldeira & Guilherme V. Moura & Francisco J. Nogales & André A. P. Santos, 2017. "Combining Multivariate Volatility Forecasts: An Economic-Based Approach," Journal of Financial Econometrics, Oxford University Press, vol. 15(2), pages 247-285.
    10. Asai, Manabu & Chang, Chia-Lin & McAleer, Michael, 2022. "Realized matrix-exponential stochastic volatility with asymmetry, long memory and higher-moment spillovers," Journal of Econometrics, Elsevier, vol. 227(1), pages 285-304.
    11. Roxana Halbleib & Valeri Voev, 2016. "Forecasting Covariance Matrices: A Mixed Approach," Journal of Financial Econometrics, Oxford University Press, vol. 14(2), pages 383-417.
    12. Gao, Guangyuan & Ho, Kin-Yip & Shi, Yanlin, 2020. "Long memory or regime switching in volatility? Evidence from high-frequency returns on the U.S. stock indices," Pacific-Basin Finance Journal, Elsevier, vol. 61(C).
    13. 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.
    14. Abderrazak Ben Maatoug & Rim Lamouchi & Russell Davidson & Ibrahim Fatnassi, 2018. "Modelling Foreign Exchange Realized Volatility Using High Frequency Data: Long Memory versus Structural Breaks," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 10(1), pages 1-25, March.
    15. 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.
    16. Proietti, Tommaso, 2014. "Exponential Smoothing, Long Memory and Volatility Prediction," MPRA Paper 57230, University Library of Munich, Germany.
    17. Bucci, Andrea & Palomba, Giulio & Rossi, Eduardo, 2023. "The role of uncertainty in forecasting volatility comovements across stock markets," Economic Modelling, Elsevier, vol. 125(C).
    18. Cristina Amado & Annastiina Silvennoinen & Timo Ter¨asvirta, 2018. "Models with Multiplicative Decomposition of Conditional Variances and Correlations," NIPE Working Papers 07/2018, NIPE - Universidade do Minho.
    19. Andrea BUCCI, 2017. "Forecasting Realized Volatility A Review," Journal of Advanced Studies in Finance, ASERS Publishing, vol. 8(2), pages 94-138.
    20. Shi, Yanlin & Ho, Kin-Yip, 2015. "Long memory and regime switching: A simulation study on the Markov regime-switching ARFIMA model," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 189-204.

    More about this item

    Keywords

    Long memory; Dynamic conditional correlation; Smooth structural change; Flexible Fourier form; Forecasting; Penalised MLE;
    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
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

    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:empfin:v:75:y:2024:i:c:s0927539823001305. 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/jempfin .

    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.