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Forecasting trends with asset prices

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  • Ahmed Bel Hadj Ayed
  • Gr'egoire Loeper
  • Fr'ed'eric Abergel

Abstract

In this paper, we consider a stochastic asset price model where the trend is an unobservable Ornstein Uhlenbeck process. We first review some classical results from Kalman filtering. Expectedly, the choice of the parameters is crucial to put it into practice. For this purpose, we obtain the likelihood in closed form, and provide two on-line computations of this function. Then, we investigate the asymptotic behaviour of statistical estimators. Finally, we quantify the effect of a bad calibration with the continuous time mis-specified Kalman filter. Numerical examples illustrate the difficulty of trend forecasting in financial time series.

Suggested Citation

  • Ahmed Bel Hadj Ayed & Gr'egoire Loeper & Fr'ed'eric Abergel, 2015. "Forecasting trends with asset prices," Papers 1504.03934, arXiv.org, revised Apr 2015.
    • Handle: RePEc:arx:papers:1504.03934
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    References listed on IDEAS

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    1. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
    2. Lakner, Peter, 1998. "Optimal trading strategy for an investor: the case of partial information," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 77-97, August.
    3. M. F. M. Osborne, 1959. "Brownian Motion in the Stock Market," Operations Research, INFORMS, vol. 7(2), pages 145-173, April.
    4. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    5. Y. Lemp'eri`ere & C. Deremble & P. Seager & M. Potters & J. P. Bouchaud, 2014. "Two centuries of trend following," Papers 1404.3274, arXiv.org.
    6. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-417, October.
    7. Brendle, Simon, 2006. "Portfolio selection under incomplete information," Stochastic Processes and their Applications, Elsevier, vol. 116(5), pages 701-723, May.
    8. Leroux, Brian G., 1992. "Maximum-likelihood estimation for hidden Markov models," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 127-143, February.
    9. Roberto Casarin & Jean-Michel Marin, 2007. "Online data processing: comparison of Bayesian regularized particle filters," Working Papers 0703, University of Brescia, Department of Economics.
    10. Monahan, John F., 1983. "Fully Bayesian analysis of ARMA time series models," Journal of Econometrics, Elsevier, vol. 21(3), pages 307-331, April.
    11. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
    12. 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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    Cited by:

    1. Ahmed Bel Hadj Ayed & Gr'egoire Loeper & Fr'ed'eric Abergel, 2016. "Robustness of mathematical models and technical analysis strategies," Papers 1605.00173, arXiv.org.
    2. Ahmed Belhadjayed & Grégoire Loeper & Sofiene El Aoud & Frédéric Abergel, 2017. "Performance analysis of the optimal strategy under partial information," Post-Print hal-01512432, HAL.
    3. Ahmed Bel Hadj Ayed & Grégoire Loeper & Sofiene El Aoud & Frédéric Abergel, 2017. "Performance Analysis Of The Optimal Strategy Under Partial Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-21, March.
    4. Ahmed Bel Hadj Ayed & Gr'egoire Loeper & Sofiene El Aoud & Fr'ed'eric Abergel, 2015. "Performance analysis of the optimal strategy under partial information," Papers 1510.03596, arXiv.org.

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