Fitting non-gaussian Models to Financial data: An Empirical Study

• Olivares, Pablo ^[2] ; Álvarez, Alexánder ^[1]
  1. [1] Universidad de La Habana

     Universidad de La Habana

     Cuba

     
  2. [2] Instituto de Cibernética, Matemática y Física (ICIMAF)
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 11, Nº. 1, 2004, págs. 81-93
• Idioma: inglés
• DOI: 10.15517/rmta.v11i1.239
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    En el trabajo se presentan algunas experiencias en la modelación de datos financieros usando tres clases de modelos alternativos a los modelos Gaussianos lineales. Se consoderan modelos con volatilidad dinámica, estables de Lévy y difusiones con Saltos. Las técnicas son ilustradas con ejemplos de series financieras de tasas de cambio, futuros e índices

  • English

    In this paper are presented some experiences about the modeling of financial data by three classes of models as alternative to Gaussian Linear models. Dynamic Volatility, Stable L'evy and Diffusion with Jumps models are considered. The techniques are illustrated with some examples of financial series on currency, futures and indexes.

• Referencias bibliográficas
  • Alvarez, A.; Olivares, P. (2003) “M.l.e. for diffusion with jumps from discrete observations”, Reporte de Investigación. ICIMAF, 253-2003.
  • Bollerslev, T.; Chou, R.C.; Kroner, K. (1992) “ARCH modeling in finance”, Journal of Econometrics 52: 5–59.
  • Box, G.E.; Jenkins, G.M. (1976) Time Series Analysis, Forecasting and Control. Holden-Day.
  • Engle, R.F. (1995) ARCH: Selected Readings. Oxford University Press, Oxford.
  • Cont, R. (1999) “Statistical properties of financial time series”. Symposium on Mathematical Finance Fudan University, Shanghai.
  • Fama, E.; Roll, R. (1971) “Parameters estimates for symmetric stable distributions”, Journal of the American Statistical Association 66: 331–339.
  • Jacod, J.; Shiryaev, A.N. (1987) Limit Theorems for Stochastic Processes. Springer Verlag, New York.
  • Mandelbrot, B. (1963) “The variation of certain speculative prices”, J. of Bus. 26: 394–419.
  • McCulloch, J.H. (1963) “Measuring tail thickness in order to estimate the stable index α: a critique”, Bussiness and Economic Statistics 15:...
  • Samorodnitsky, G.; Taqqu, M.S. (1994) Stable non-Gaussian Random Processes: Stochastic Models with Infinite Variance. Chapman & Hall,...
  • Seco, L.; Alvarez, A.; Escobar, M.; Olivares, P. (2003) “An overview of estimation methods for stable distributions with financial applications”,...
  • Shiriev, A.N. (1999) Essencials of Stochastic Finance. World Scientific, Singapur.
  • Sørensen, M. (1990) “Likelihood methods for diffusions with jumps”, Statistical Inference in Stochastic Processes. N.U. Prabhu & I.V....
  • Weron R. (s.f.) “Performance of the etimators of stable laws”, Working paper.