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ABC and Hamiltonian Monte-Carlo methods in COGARCH models

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  • Marín Díazaraque, Juan Miguel
  • 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

  • Marín Díazaraque, Juan Miguel & 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
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    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..
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    Keywords

    Approximate Bayesian Computation methods (ABC);

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