Etude de la dynamique non-linéaire des rentabilités de la bourse de Casablanca

RIANE, Nizare (2014): Etude de la dynamique non-linéaire des rentabilités de la bourse de Casablanca.

Abstract

The preponderance of the linear approach in the stock market modeling is the result of the Frisch-Slutsky paradigm which implies that the market can only converge to an equilibrium point or diverge, according to a monotonic or oscillatory trajectory. Moreover, this description of reality is insufficient, first by his inability to describe the fluctuations that tend to persist and market anomalies, second by the weakness of the linear statistical tests facing more complex processes. In this paper, we examine the existence of a non-linear dynamics that govern the evolution of the MASI Index. The analysis uses the concepts of Lyapunov exponents, correlation dimension and other tools to determine the nature of the underlying process. The results provide evidence of a non-linear process, but the determinism remains contested.

• Item Type: MPRA Paper
• English Title: Study of the returns nonlinear dynamics of the Casablanca stock exchange
• Language: French
• Keywords: Chaos, attractor, nonlinearity, determinism, Lyapunov exponent, correlation dimension.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C19 - Other; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates

References

Arnold L. (23 avril 1974), Stochastic Differential Equations: Theory and Applications, Wiley Interscience, 1ère édition.

Bakker R., Schouten C., Coppens M-C., Takens F., Lee Giles C. et Van Den Bleek M. (2000), « Robust Learning of Chaotic Attractors », MIT Press, pp. 879—885.

Bonache A. (2008), « Les ventes de produits innovants à la mode sont-elles chaotiques ? Le cas des ventes de Game Boy au Japon », Munich Personal RePEc Archive.

Brock W., Dechert W.D., Scheinkman J. et Lebaron B. (1991), « A test for independence based on the correlation dimension », Econometric Reviews, vol.15, n°3.

Brusse M. et Weihs C. (2004), « Lyapunov Exponent for Stochastic Time Series ».

Campbell J. Y., Lo A. W. et Mackinlay A. C. (9 décembre 1996), The Econometrics of Financial Markets, Princeton University Press.

Casdagli M. (1992), « Chaos and Deterministic versus Stochastic Non-Linear Modeling », Journal of the Royal Statistical Society, Series B (Methodological), Vol. 54, No. 2, pp. 303-328

Chan K. S. et Tong H. (1994), « A Note on Noisy Chaos », Journal of the Royal Statistical Society. Series B (Methodological), Vol. 56, No. 2, pp. 301-311.

Dennis B., Desharnais A., Cushing J. M., Henson M. et Constantin R. F. (2003), « Can noise induce chaos? », Oikos 102, pp. 329–339.

Eckmann J.-P., Kamphorst O., Ruelle D. et Ciliberto S. (1986), « Lyapunov Exponent from time series », Physical Review A, Vol. 34, No. 6.

Eckmann J.-P. et Ruelle D. (1985), « Ergodic Theory of Chaos and Strang Attractor », Reviews of Modern Physics, Vol. 57, No. 3, Part 1.

Enescu B., Ito K., et Struzik Z. R. (2004), « Wavelet-Based Multifractal Analysis of Real and Simulated Time Series of Earthquakes », Annuals of Disas. Prev. Res. Inst., Kyoto Univ., No. 47 B.

Franses P. H. et Van Dijk D. (4 septembre 2000), Nonlinear Time Series Models in Empirical Finance, Cambridge University Press, 1ère édition.

Girerd-Potin I. et Taramasco O. (1994), « Les rentabilités à la bourse de Paris sont-elles chaotiques ? », Revue économique, Volume 45, Numéro 2, pp. 215 – 238.

Grassberger P. et Procaccia I. (1983), « Estimation of the Kolmogorov Entropy from Chaotic Signal », Physical Review A, Vol. 28, No. 4.

Guégan D. (2003), Les Chaos en Finance : Approche Statistique, Economica.

Gundlash M. (1991), « Chaos in Random Dynamical Systems ».

Halsey C., Jensen H., Kadanoff P., Procaccia I. et Shraiman I. (1985), « Fractal Measures and their Singularities, The Characterization of Strange Sets », Physical Review A, Vol. 33, No. 2.

Kantz H., Schreiber T. (26 janvier 2004), Nonlinear Time Series Analysis, Cambridge University Press, 2ème édition.

Kaplan T. (1994), « Exceptional Events as Evidence for Determinism », Physica D 73: 38-48.

Kennel B., Brown R. et Abarbanel D. I. (1991), « Determining Embedding Dimension for Phase-space Reconstruction Using a Geometrical Construction », Physical Review A, Vol. 45 No. 6.

Marwan N., Romano M. C., Thiel M. et Kurths J. (2006), « Recurrence Plots for the Analysis of Complex Systems », Physics Reports 438, pp. 237 – 329.

NELSON C. ZIVOT E. ET PIGER J. M. (2001) « Markov Regime Switching and Unit Root Tests », Federal Reserve Bank of ST. LOUIS.

Peters E. E. (1991), « A Chaotic Attractor for the S&P 500 », Financial Analysts Journal, Vol. 47, No. 2, pp. 55-62+81.

Peters E. E (12 janvier 1994), Fractal Market Analysis: Applying Chaos Theory to Investment and Economics, Wiley, 1ère édition.

Peters E. E. (août 1996), Order and Chaos in the Capital Market: a New View of Cycles, Prices, and Market Volatility, Wiley, 2ème édition.

Parlitz U. (1992), « Identification of True and Spurious Lyapunov Exponents from Time Series », International journal of bifurcation and chaos, Vol. 2, No. 1, pp. 155-165.

Priestley M. B. et Subba Rao T. (1969), « A Test for Non-Stationarity of Time-Series », Journal of the Royal Statistical Society. Series B (Methodological), Vol. 31, No. 1, pp. 140-149

Schreiber T. et Schmitz A. (1997), « Discrimination power of measures for nonlinearity in a time series », Physical Review E, Vol. 55, No. 5.

So P., Ott E., Schiff J., Kaplan T., Sauer T. et Grebogi C. (1995), « Detecting Unstable Periodic Orbits in Chaotic Experimental Data », Physical Review letters, Vol. 76, No. 25.

Strozzi F. (2002), « Application of Non-Linear Time Series Analysis Techniques to High Frequency Currency Exchange Data », Liuc Papers n. 99, Serie Metodi quantitative 14.

Theiller J. (1987), « Efficient Algorithm for Estimating the Correlation Dimension from a Set of Discrete Points », Physical Review A, Vol. 36, No. 9.