IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v223y2024icp543-564.html
   My bibliography  Save this article

Time series clustering based on latent volatility mixture modeling with applications in finance

Author

Listed:
  • Setoudehtazangi, F.
  • Manouchehri, T.
  • Nematollahi, A.R.
  • Caporin, M.

Abstract

Modeling financial time series data poses a significant challenge in the realm of time series analysis. The Autoregressive Conditional Heteroskedasticity (ARCH) model stands out as a potent tool for capturing time-varying volatility and heteroskedasticity in financial data. However, conventional ARCH models display sensitivity to departures from normality, leading to the development of extensions employing more flexible distributions. In this context, we propose a robust enhancement to the mixture of ARCH (MoARCH) model by integrating normal mean–variance mixture (NMVM) distributions to model component errors. The stochastic representation of the proposed model allows for a straightforward implementation of an Expectation Conditional Maximization Either (ECME) algorithm for obtaining Maximum Penalized Likelihood estimates (MPL). To thoroughly evaluate the model, we conduct four simulation studies to explore finite-sample properties, assess MPL estimators, scrutinize model robustness, and evaluate the accuracy of our proposal in fitting, clustering, and forecasting. Practical applications further highlight the effectiveness of our methodology, showcasing successful implementations across diverse real datasets.

Suggested Citation

  • Setoudehtazangi, F. & Manouchehri, T. & Nematollahi, A.R. & Caporin, M., 2024. "Time series clustering based on latent volatility mixture modeling with applications in finance," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 543-564.
    • Handle: RePEc:eee:matcom:v:223:y:2024:i:c:p:543-564
    DOI: 10.1016/j.matcom.2024.04.031
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475424001575
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2024.04.031?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. Bollerslev, Tim & Russell, Jeffrey & Watson, Mark (ed.), 2010. "Volatility and Time Series Econometrics: Essays in Honor of Robert Engle," OUP Catalogue, Oxford University Press, number 9780199549498.
    2. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    3. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    4. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
    7. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
    8. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
    9. 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.
    10. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    11. Vilca, Filidor & Balakrishnan, N. & Zeller, Camila Borelli, 2014. "Multivariate Skew-Normal Generalized Hyperbolic distribution and its properties," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 73-85.
    12. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    13. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    14. Benny Ren & Ian Barnett, 2022. "Autoregressive mixture models for clustering time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(6), pages 918-937, November.
    15. Shima Ghassempour & Federico Girosi & Anthony Maeder, 2014. "Clustering Multivariate Time Series Using Hidden Markov Models," IJERPH, MDPI, vol. 11(3), pages 1-23, March.
    16. Stanley Sclove, 1987. "Application of model-selection criteria to some problems in multivariate analysis," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 333-343, 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. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    2. Dennis Kristensen, 2009. "On stationarity and ergodicity of the bilinear model with applications to GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 125-144, January.
    3. Błażej Mazur & Mateusz Pipień, 2012. "On the Empirical Importance of Periodicity in the Volatility of Financial Returns - Time Varying GARCH as a Second Order APC(2) Process," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 4(2), pages 95-116, June.
    4. 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.
    5. Xibin Zhang & Maxwell L. King, 2013. "Gaussian kernel GARCH models," Monash Econometrics and Business Statistics Working Papers 19/13, Monash University, Department of Econometrics and Business Statistics.
    6. Beutner, Eric & Heinemann, Alexander & Smeekes, Stephan, 2024. "A residual bootstrap for conditional Value-at-Risk," Journal of Econometrics, Elsevier, vol. 238(2).
    7. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107630024.
    8. Emma M. Iglesias & Garry D. A. Phillips, 2012. "Estimation, Testing, and Finite Sample Properties of Quasi-Maximum Likelihood Estimators in GARCH-M Models," Econometric Reviews, Taylor & Francis Journals, vol. 31(5), pages 532-557, September.
    9. Yuanyuan Zhang & Rong Liu & Qin Shao & Lijian Yang, 2020. "Two‐Step Estimation for Time Varying Arch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 551-570, July.
    10. Wang, Hui & Pan, Jiazhu, 2014. "Normal mixture quasi maximum likelihood estimation for non-stationary TGARCH(1,1) models," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 117-123.
    11. Todd Prono, 2016. "Closed-Form Estimation of Finite-Order ARCH Models: Asymptotic Theory and Finite-Sample Performance," Finance and Economics Discussion Series 2016-083, Board of Governors of the Federal Reserve System (U.S.).
    12. Prono Todd, 2018. "Closed-form estimators for finite-order ARCH models as simple and competitive alternatives to QMLE," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(5), pages 1-25, December.
    13. Kristensen Dennis & Rahbek Anders, 2009. "Asymptotics of the QMLE for Non-Linear ARCH Models," Journal of Time Series Econometrics, De Gruyter, vol. 1(1), pages 1-38, April.
    14. Eric Beutner & Julia Schaumburg & Barend Spanjers, 2024. "Bootstrapping GARCH Models Under Dependent Innovations," Tinbergen Institute Discussion Papers 24-008/III, Tinbergen Institute.
    15. E. Ramos-P'erez & P. J. Alonso-Gonz'alez & J. J. N'u~nez-Vel'azquez, 2020. "Forecasting volatility with a stacked model based on a hybridized Artificial Neural Network," Papers 2006.16383, arXiv.org, revised Aug 2020.
    16. M. Jiménez Gamero, 2014. "On the empirical characteristic function process of the residuals in GARCH models and applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 409-432, June.
    17. Zhu, Ke & Ling, Shiqing, 2013. "Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA-GARCH/IGARCH models," MPRA Paper 51509, University Library of Munich, Germany.
    18. Gorgi, P. & Koopman, S.J., 2023. "Beta observation-driven models with exogenous regressors: A joint analysis of realized correlation and leverage effects," Journal of Econometrics, Elsevier, vol. 237(2).
    19. Hu, Shuowen & Poskitt, D.S. & Zhang, Xibin, 2021. "Bayesian estimation for a semiparametric nonlinear volatility model," Economic Modelling, Elsevier, vol. 98(C), pages 361-370.
    20. Feiyu Jiang & Dong Li & Ke Zhu, 2019. "Adaptive inference for a semiparametric generalized autoregressive conditional heteroskedasticity model," Papers 1907.04147, arXiv.org, revised Oct 2020.

    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:matcom:v:223:y:2024:i:c:p:543-564. 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.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.