Analysis of intra-day fluctuations in the Mexican financial market index

L. Alfonso, D. E. Garcia-Ramirez, R. Mansilla, C. A. Terrero-Escalante


In this paper, a statistical analysis of high frequency fluctuations of the IPC, the Mexican Stock Market Index, is presented. A sample of tick--to--tick data covering the period from January 1999 to December 2002 was analyzed, as well as several other sets obtained using temporal aggregation. Our results indicates that the highest frequency is not useful to understand the Mexican market because almost two thirds of the information corresponds to inactivity. For the frequency where fluctuations start to be relevant, the IPC data does not follows any $\alpha$-stable distribution, including the Gaussian, perhaps because of the presence of autocorrelations. For a long range of lower-frequencies, but still in the intra-day regime, fluctuations can be described as a truncated L\'evy flight, while for frequencies above two-days, a Gaussian distribution yields the best fit. Thought these results are consistent with other previously reported for several  markets, there are significant differences in the details of the corresponding descriptions.


complex systems, financial dynamics, high frequency fluctuations distribution, tail behavior, autocorrelations

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E. F. Fama, Efficient capital markets: II, J. Finance, 46 1575–613 (1991)

R. N. Mantegna and H. E. Stanley, An introduction to econophysics: correlations and complexity in finance., (Cambridge University Press, New York, (1999))

P. Lévy, Calcul des Probabilites, (Paris : Gauthier-Villars et Cie, (1925))

B. B. Mandelbrot, The variation of certain speculative prices, Journal of Business 36, 394 (1963).

R. N. Mantegna and H. E. Stanley, Scaling behaviour in the dynamics of an economic index, Nature 376 46 (1995).

P. Gopikrishnan, V. Plerou, L. A. N. Amaral, M. Meyer, and H. E. Stanley , Scaling of the distribution of fluctuations of financial market indices, Phys. Rev. E 60, 5305–5316 (1999)

Cont, R., Empirical properties of asset returns: stylized facts and statistical issues, Quantitative Finance, 1: 223-236, (2001)

L. Alfonso, R. Mansilla, and C.A. Terrero-Escalante, On the scaling of the distribution of daily price fluctuations in the Mexican financial market index, Physica A: Statistical Mechanics and its Applications 391, 2990–2996 (2012).

R. N. Mantegna and H. E. Stanley, Stochastic process with ultraslow convergence to a Gaussian: the truncated Lévy flight, Physical Review Letters, 73 22, 2946 (1994).

I. Koponen, Analytic approach to the problem of convergence of truncated Lévy flights towards the Gaussian stochastic process, Phys. Rev. E 52, 1197 (1995)

T. G. Andersen, Some Reflections on Analysis of High-Frequency Data, Journal of Business and Economic Statistics 18, no. 2 (2000): 146-53. doi:10.2307/1392552.

R. Weron, Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime, International Journal of Modern Physics C 12 2 (2001).

G. Samorodnitsky and M. S. Taqqu, Stable Non-Gaussian Random Processes. Stochastic Models with Infinite Variance., (Chapman and Hall, New York - London (1994))

R. Cont, M. Potters, J. P. Bouchaud, Scale Invariance and Beyond. (Centre de Physique des Houches, vol 7. Springer, Berlin, Heidelberg (1997))

A. Matacz, Financial modeling and option theory with the truncated Lévy process, International Journal of Theoretical and Applied Finance, 3 (01), 143-160 (2000).

L. C. Miranda, and R. Riera, Truncated Lévy walks and an emerging market economic index, Physica A: Statistical Mechanics and its Applications, 297 (3-4), 509-520 (2001).



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