Analysis of effciency in high-frequency digital markets using the Hurst exponent


  • Mario López Pérez UNAM
  • R. Mansilla UNAM



Efficiency, high-frequency trading, Hurst exponent


In this paper we analyze the Effcient Market Hypothesis for automated high-frequency stock markets. Using the Hurst exponent as a measure of eciency, we show that the time series of highfrequency stock prices do not follow random walks, rejecting then (as we discuss in the text) the EMH for these markets.


L. Bachelier, Theorie de la Speculation , (Annales de l’Ecole Normale Superieure, Ser 3, Gauthier-Villars, Paris, 1900).

R. N. Mantegna, H. E. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance, (Cambridge University Press, UK, 2000).

R. Mansilla, Una breve introduccion a la Econof ´ ´ısica, (Equipo Sirius, S. A., Madrid, Espana, 2003).

H. K. Pharasi, K. Sharma, R. Chatterjee, A. Chakraborti, F. Leyvraz, T. H. Seligman, Identifying long-term precursors of financial market crashes using correlation patterns, New Journal of Physics 20 (2018) 103041,

A. Chakraborti, K. Sharma, H. K. Pharasi, K. Shuvo Bakar, S. Das, T. H. Seligman, Emerging spectra characterization of catastrophic instabilities in complex systems, New Journal of Physics 22 (2020) 063043,

K. Kanazawa, T. Sueshige, H. Takayasu, M. Takayasu, Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders, Physical Review Letters 120 (2018) 138301,

E. Fama, The Behavior of Stock Market Prices, The Journal of Business, 38 (1965) 34,

A. W. Lo, A. C. MacKinlay, A Non-Random Walk Down Wall Street, (Princeton University Press, Princeton, New Jersey, 1999), pp. 10.

J. L. McCauley, Dynamics of Markets, The New Financial Economics, second edition, (Cambridge University Press, New York, 2009), pp. 10-29.

J. Keynes, The General Theory of Employment, Interest and Money, (Palgrave Macmillan, London, 1936), pp. 161-162.

H. Simon, A Behavioral Model of Rational Choice, The QuarRev. Mex. Fis. 67 061401 ANALYSIS OF EFFICIENCY IN HIGH-FREQUENCY DIGITAL MARKETS USING THE HURST EXPONENT 11 terly Journal of Economics 69 (1955) 99,

A. W. Lo, The Adaptative Market Hypothesis, The Journal of Portfolio Management 30th Anniversary 30 (2004) 15,

S. Leroy, Risk aversion and the martingale property of stocks rerturns, International Economic Review 14 (1973) 436,

R. Lucas, Asset prices in an exchange economy, Econometrika 46 (1978) 1429,

H. E. Hurst, Long-Term Storage Capacity of Reservoirs, Transactions of the American Society of Civil Engineers 116 (1951) 770,

B. B. Mandelbrot, J. R. Wallis, Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence, Water Resources Research 5 (1969) 967,

G. Wang, G. Antar, P. Devynck, The Hurst exponent and longtime correlation, Physics of Plasmas 7 (2000) 1181, https://doi:10.1063/1.873927.

C.-F. Li, Rescaled-range and power spectrum analyses on welllogging data, Geophysical Journal International 153 (2003) 201,

M. A. Sanchez, J. E. Trinidad, J. Garc ´ ´ıa, M. Fernandez, ´ The Effect of the Underlying Distribution in Hurst Exponent Estimation, PLoS ONE 10 (2015) e0127824, https://doi:10.1371/journal.pone.0127824.

A. W. Lo, Long-Term Memory in Stock Market Prices, Econometrica 59 (1991) 1279,

W. Willinger, M. S. Taqqu, V. Teverovsky, Stock market prices and long-range dependence, Finance Stochast. 3 (1999) 1,

J. Barunik, L. Kristoufek, On Hurst exponent estimation under heavy-tailed distributions, Physica A: Statistical Mechanics and its Applications 389 (2010) 3844,

D. O. Cajueiro, B. M. Tabak, The Hurst exponent over time: testing the assertion that emerging markets are becoming more

effcient, Physica A: Statistical Mechanics and its Applications 336 (2004) 521,

Ch. Eom, S. Choi, G. Oh, W. Jung Hurst exponent and prediction based on weak-form efficient market hypothesis of stock markets, Physica A: Statistical Mechanics and its Applications 387 (2008) 4630,

D. Grech, Z. Mazur, Can one make any crash prediction in finance using the local Hurst exponent idea?, Physica A: Statistical Mechanics and its Applications 336 (2004) 133,

E. Peters, Fractal Market Analysis. Applying Chaos Theory to Investment and Economics, (John Wiley and Sons, INC., New York, 1994) pp. 39-85.

M.A. Sanchez, J.E. Trinidad, J. Garc ´ ´ıa, Some comments on Hurst exponent and the long memory processes on capital markets, Physica A: Statistical Mechanics and its Applications 387 (2008) 5543,




How to Cite

M. López Pérez and R. Mansilla, “Analysis of effciency in high-frequency digital markets using the Hurst exponent”, Rev. Mex. Fís., vol. 67, no. 6 Nov-Dec, pp. 061402 1–, Nov. 2021.



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