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Monte Carlo likelihood inference for marked doubly stochastic Poisson processes with intensity driven by marked point processes

Author

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  • Marco Minozzo

    (Department of Economics (University of Verona))

  • Silvia Centanni

    (Department of Economics (University of Verona))

Abstract

In recent years, marked point processes have found a natural application in the modeling of ultra-high-frequency financial data since they do not require the integration of the data which is usually needed by other modeling approaches. Among these processes, two main classes have so far been proposed to model financial data: the class of autoregressive conditional duration models of Engle and Russel and the broad class of doubly stochastic Poisson processes with marks. In this paper we consider a class of marked doubly stochastic Poisson processes in which the intensity is driven by another marked point process. In particular, we focus on an intensity with a shot noise form that can be interpreted in terms of the effect caused by news arriving on the market. For models in this class we study likelihood inferential procedures such as Monte Carlo likelihood and importance sampling Monte Carlo expectation maximization by making use of reversible jump Markov chain Monte Carlo algorithms.

Suggested Citation

  • Marco Minozzo & Silvia Centanni, 2012. "Monte Carlo likelihood inference for marked doubly stochastic Poisson processes with intensity driven by marked point processes," Working Papers 11/2012, University of Verona, Department of Economics.
    • Handle: RePEc:ver:wpaper:11/2012
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    References listed on IDEAS

    as
    1. Pearce, Douglas K & Roley, V Vance, 1985. "Stock Prices and Economic News," The Journal of Business, University of Chicago Press, vol. 58(1), pages 49-67, January.
    2. Luc Bauwens & Nikolaus Hautsch, 2006. "Stochastic Conditional Intensity Processes," Journal of Financial Econometrics, Oxford University Press, vol. 4(3), pages 450-493.
    3. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    4. Gareth O. Roberts & Omiros Papaspiliopoulos & Petros Dellaportas, 2004. "Bayesian inference for non‐Gaussian Ornstein–Uhlenbeck stochastic volatility processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 369-393, May.
    5. Rüdiger Frey & Wolfgang J. Runggaldier, 2001. "A Nonlinear Filtering Approach To Volatility Estimation With A View Towards High Frequency Data," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 199-210.
    6. Dassios, Angelos & Jang, Jiwook, 2003. "Pricing of catastrophe reinsurance and derivatives using the Cox process with shot noise intensity," LSE Research Online Documents on Economics 2849, London School of Economics and Political Science, LSE Library.
    7. Centanni, Silvia & Minozzo, Marco, 2006. "A Monte Carlo Approach to Filtering for a Class of Marked Doubly Stochastic Poisson Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1582-1597, December.
    8. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    9. Kalev, Petko S. & Liu, Wai-Man & Pham, Peter K. & Jarnecic, Elvis, 2004. "Public information arrival and volatility of intraday stock returns," Journal of Banking & Finance, Elsevier, vol. 28(6), pages 1441-1467, June.
    10. repec:bla:jfinan:v:53:y:1998:i:1:p:219-265 is not listed on IDEAS
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    Cited by:

    1. Alan Genaro & Adilson Simonis, 2015. "Estimating doubly stochastic Poisson process with affine intensities by Kalman filter," Statistical Papers, Springer, vol. 56(3), pages 723-748, August.

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    More about this item

    Keywords

    Cox process; marked point process; reversible jump Markov chain Monte Carlo; shot noise process; ultra-high-frequency data;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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