Identifying a Non-normal Evolving Stochastic Process Based upon the Genetic Methods

  • Kangrong Tan
  • Meifen Chu
  • Shozo Tokinaga
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7027)


In the real world, many evolving stochastic processes appear heavy tails, excess kurtosis, and other non-normal evidences, though, they eventually converge to normals due to the central limit theorem, and the augment effect.

So far many studies focusing on the normal cases, such as Brownian Motion, or Geometric Brownian Motion etc, have shown their restrictions in dealing with non-normal phenomena, although they have achieved a great deal of success. Moreover, in many studies, the statistical properties, such as the distributional parameters of an evolving process, have been studied at a special time spot, not having grasped the whole picture during the whole evolving time period.

In this paper, we propose to approximate an evolving stochastic process based upon a process characterized by a time-varying mixture distribution family to grasp the whole evolving picture of its evolution behavior. Good statistical properties of such a time-varying process are well illustrated and discussed. The parameters in such a time-varying mixture distribution family are optimized by the Genetic Methods, namely, the Genetic Algorithm (GA) and Genetic Programming (GP). Numerical experiments are carried out and the results prove that our proposed approach works well in dealing with a non-normal evolving stochastic process.


Genetic Algorithm Genetic Method Markov Chain Monte Carlo Method Mixture Distribution Geometric Brownian Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Titterington, D., Smith, A., Makov, U.: Statistical Analysis of Finite Mixture Distributions. John Wiley and Sons (1985)Google Scholar
  2. 2.
    Tan, K., Tokinaga, S.: Identifying returns distribution by using mixture distribution optimized by genetic algorithm. In: Proceedings of NOLTA 2006, pp. 119–122 (2006)Google Scholar
  3. 3.
    McLachlan, G.J., Basford, K.E.: Mixture Models: Inference and Applications to Clustering. Marcel Dekker (1988)Google Scholar
  4. 4.
    Carol, A.: Normal mixture diffusion with uncertain volatility: Modelling short and long-term smile effects. Journal of Banking & Finance 28(12) (2004)Google Scholar
  5. 5.
    Tan, K.: An Approximation of returns distribution based upon GA optimized mixture distribution and its applications. In: Proceedings of the Fourth International Conference on Computational Intelligence, Robotics and Autonomous Systems, pp. 307–312 (2007)Google Scholar
  6. 6.
    Carlin, B.P., Louis, T.A.: Bayes and empirical Bayes methods for data analysis. Chapman and Hall, New York (1996)zbMATHGoogle Scholar
  7. 7.
    Clifford, P.: Discussion on the meeting on the Gibbs sampler and other Markov chain Monte Carlo methods. Journal of the Royal Statistical Society, Series B 55, 53–54 (1993)MathSciNetGoogle Scholar
  8. 8.
    Goldberg, D.E.: Genetic Algorithm: in Search, Optimization, and Machine Learning. Addison-Wesley Press (1989)Google Scholar
  9. 9.
    Koza, J.R.: Genetic Programming. MIT Press (1992)Google Scholar
  10. 10.
    Tan, K., Gani, J.: Theoretical Advances and Applications in Operatios Research. Kyushu University Press (2011)Google Scholar
  11. 11.
    Dorsey, B., Mayer, W.J.: Genetic algorithms for estimation problems with multiple optima, nondifferentiability and other irregular features. Journal of Business and Economic Statistics 13, 53–66 (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Kangrong Tan
    • 1
  • Meifen Chu
    • 2
  • Shozo Tokinaga
    • 3
  1. 1.Department of EconomicsKurume UniversityKurume CityJapan
  2. 2.Department of EconomicsKyushu UniversityFukuoka CityJapan
  3. 3.Graduate School of EconomicsKyushu UniversityFukuokaJapan

Personalised recommendations