IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/ws1601.html
   My bibliography  Save this paper

ABC and Hamiltonian Monte-Carlo methods in COGARCH models

Author

Listed:
  • Rodríguez-Bernal, M. T.
  • Romero, E.

Abstract

The analysis of financial series, assuming calendar effects and unequally spaced times over continuous time, can be studied by means of COGARCH models based on Lévy processes. In order to estimate the COGARCH model parameters, we propose to use two different Bayesian approaches. First, we suggest to use a Hamiltonian Montecarlo (HMC) algorithm that improves the performance of standard MCMC methods. Secondly, we introduce an Approximate Bayesian Computational (ABC) methodology which allows to work with analytically infeasible or computationally expensive likelihoods. After a simulation and comparison study for both methods, HMC and ABC, we apply them to model the behaviour of some NASDAQ time series and we discuss the results.

Suggested Citation

  • Rodríguez-Bernal, M. T. & Romero, E., 2016. "ABC and Hamiltonian Monte-Carlo methods in COGARCH models," DES - Working Papers. Statistics and Econometrics. WS ws1601, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws1601
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/rest/api/core/bitstreams/e956a579-958d-4edf-9da1-4ee898848470/content
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. McKinley Trevelyan & Cook Alex R & Deardon Robert, 2009. "Inference in Epidemic Models without Likelihoods," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-40, July.
    2. S. Haug & C. Klüppelberg & A. Lindner & M. Zapp, 2007. "Method of moment estimation in the COGARCH(1,1) model," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 320-341, July.
    3. Ross A. Maller & Gernot Muller & Alex Szimayer, 2008. "GARCH modelling in continuous time for irregularly spaced time series data," Papers 0805.2096, arXiv.org.
    4. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    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. Rodríguez Bernal, M. T. & Romero, Eva, 2013. "Data cloning estimation of GARCH and COGARCH models," DES - Working Papers. Statistics and Econometrics. WS ws132723, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. P. Brockwell, 2014. "Recent results in the theory and applications of CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 647-685, August.
    3. Enrico Bibbona & Ilia Negri, 2015. "Higher Moments and Prediction-Based Estimation for the COGARCH(1,1) Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 891-910, December.
    4. Thiago do Rêgo Sousa & Robert Stelzer, 2022. "Moment‐based estimation for the multivariate COGARCH(1,1) process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 681-717, June.
    5. Lee, Oesook, 2012. "V-uniform ergodicity of a continuous time asymmetric power GARCH(1,1) model," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 812-817.
    6. Anatoliy Swishchuk, 2013. "Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8660, August.
    7. Paul Ormerod, 2010. "La crisis actual y la culpabilidad de la teoría macroeconómica," Revista de Economía Institucional, Universidad Externado de Colombia - Facultad de Economía, vol. 12(22), pages 111-128, January-J.
    8. Dominique Guégan & Wayne Tarrant, 2012. "On the necessity of five risk measures," Annals of Finance, Springer, vol. 8(4), pages 533-552, November.
    9. Alagidede, Paul & Panagiotidis, Theodore, 2009. "Modelling stock returns in Africa's emerging equity markets," International Review of Financial Analysis, Elsevier, vol. 18(1-2), pages 1-11, March.
    10. Ben Klemens, 2013. "A Peer-based Model of Fat-tailed Outcomes," Papers 1304.0718, arXiv.org.
    11. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
    12. Geluk, J.L. & De Vries, C.G., 2006. "Weighted sums of subexponential random variables and asymptotic dependence between returns on reinsurance equities," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 39-56, February.
    13. Erie Febrian & Aldrin Herwany, 2009. "Volatility Forecasting Models and Market Co-Integration: A Study on South-East Asian Markets," Working Papers in Economics and Development Studies (WoPEDS) 200911, Department of Economics, Padjadjaran University, revised Sep 2009.
    14. Vianna Franco, Marco P. & Ribeiro, Leonardo Costa & Albuquerque, Eduardo da Motta e, 2022. "Beyond Random Causes: Harmonic Analysis Of Business Cycles At The Moscow Conjuncture Institute," Journal of the History of Economic Thought, Cambridge University Press, vol. 44(3), pages 456-476, September.
    15. de Lima, Pedro J. F., 1997. "On the robustness of nonlinearity tests to moment condition failure," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 251-280.
    16. P. Kearns & A.R. Pagan, 1993. "Australian Stock Market Volatility: 1875–1987," The Economic Record, The Economic Society of Australia, vol. 69(2), pages 163-178, June.
    17. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
    18. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    19. Runde, Ralf & Scheffner, Axel, 1998. "On the existence of moments: With an application to German stock returns," Technical Reports 1998,25, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    20. Chen, Zhimin & Ibragimov, Rustam, 2019. "One country, two systems? The heavy-tailedness of Chinese A- and H- share markets," Emerging Markets Review, Elsevier, vol. 38(C), pages 115-141.

    More about this item

    Keywords

    Approximate Bayesian Computation methods (ABC);

    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:cte:wsrepe:ws1601. 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: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    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.