<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2021000600011</article-id>
<article-id pub-id-type="doi">10.31349/revmexfis.67.061402</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Analysis of efficiency in high-frequency digital markets using the Hurst exponent]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[López]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Mansilla]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional Autónoma de México Facultad de Ciencias ]]></institution>
<addr-line><![CDATA[Ciudad de México ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Nacional Autónoma de México Centro de Investigaciones Interdisciplinarias en Ciencias y Humanidades ]]></institution>
<addr-line><![CDATA[Ciudad de México ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<volume>67</volume>
<numero>6</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2021000600011&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2021000600011&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2021000600011&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In this paper, we analyze the Efficient Market Hypothesis for automated high-frequency stock markets. Using the Hurst exponent as a measure of efficiency, we show that the time series of high-frequency stock prices do not follow random walks, rejecting then (as we discuss in the text) the EMH for these markets.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Efficiency]]></kwd>
<kwd lng="en"><![CDATA[high-frequency trading]]></kwd>
<kwd lng="en"><![CDATA[Hurst exponent]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bachelier]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Théorie de la Spéculation]]></source>
<year>1900</year>
<edition>3</edition>
<publisher-loc><![CDATA[Gauthier-Villars, Paris ]]></publisher-loc>
<publisher-name><![CDATA[Annales de l&#8217;Ecole Normale Supérieure]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mantegna]]></surname>
<given-names><![CDATA[R. N.]]></given-names>
</name>
<name>
<surname><![CDATA[Stanley]]></surname>
<given-names><![CDATA[H. E.]]></given-names>
</name>
</person-group>
<source><![CDATA[An Introduction to Econophysics: Correlations and Complexity in Finance]]></source>
<year>2000</year>
<publisher-loc><![CDATA[UK ]]></publisher-loc>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mansilla]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Una breve introducción a la Econofísica]]></source>
<year>2003</year>
<publisher-loc><![CDATA[Madrid, España ]]></publisher-loc>
<publisher-name><![CDATA[Equipo Sirius, S. A]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pharasi]]></surname>
<given-names><![CDATA[H. K.]]></given-names>
</name>
<name>
<surname><![CDATA[Sharma]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Chatterjee]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Chakraborti]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Leyvraz]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Seligman]]></surname>
<given-names><![CDATA[T. H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Identifying long-term precursors of financial market crashes using correlation patterns]]></article-title>
<source><![CDATA[New Journal of Physics]]></source>
<year>2018</year>
<volume>20</volume>
<page-range>103041</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chakraborti]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Sharma]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Shuvo Pharasi]]></surname>
<given-names><![CDATA[H. K.]]></given-names>
</name>
<name>
<surname><![CDATA[Bakar]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Das]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Seligman]]></surname>
<given-names><![CDATA[T. H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Emerging spectra characterization of catastrophic instabilities in complex systems]]></article-title>
<source><![CDATA[New Journal of Physics]]></source>
<year>2020</year>
<volume>22</volume>
<page-range>063043</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kanazawa]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Sueshige]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Takayasu]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Takayasu]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders]]></article-title>
<source><![CDATA[Physical Review Letters]]></source>
<year>2018</year>
<volume>120</volume>
<page-range>138301</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fama]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Behavior of Stock Market Prices]]></article-title>
<source><![CDATA[The Journal of Business]]></source>
<year>1965</year>
<volume>38</volume>
<page-range>34</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>8</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lo]]></surname>
<given-names><![CDATA[A. W.]]></given-names>
</name>
<name>
<surname><![CDATA[MacKinlay]]></surname>
<given-names><![CDATA[A. C.]]></given-names>
</name>
</person-group>
<source><![CDATA[A Non-Random Walk Down Wall Street]]></source>
<year>1999</year>
<page-range>10</page-range><publisher-loc><![CDATA[Princeton, New Jersey ]]></publisher-loc>
<publisher-name><![CDATA[Princeton University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<label>9</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[McCauley]]></surname>
<given-names><![CDATA[J. L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Dynamics of Markets, The New Financial Economics]]></source>
<year>2009</year>
<edition>second</edition>
<page-range>10-29</page-range><publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<label>10</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Keynes]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[The General Theory of Employment, Interest and Money]]></source>
<year>1936</year>
<page-range>161-2</page-range><publisher-loc><![CDATA[London ]]></publisher-loc>
<publisher-name><![CDATA[Palgrave Macmillan]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<label>11</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Simon]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A Behavioral Model of Rational Choice]]></article-title>
<source><![CDATA[The Quarterly Journal of Economics]]></source>
<year>1955</year>
<volume>69</volume>
<page-range>99</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>12</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lo]]></surname>
<given-names><![CDATA[A. W.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Adaptative Market Hypothesis]]></article-title>
<source><![CDATA[The Journal of Portfolio Management 30th Anniversary]]></source>
<year>2004</year>
<volume>30</volume>
<page-range>15</page-range></nlm-citation>
</ref>
<ref id="B13">
<label>13</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Leroy]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Risk aversion and the martingale property of stocks rerturns]]></article-title>
<source><![CDATA[International Economic Review]]></source>
<year>1973</year>
<volume>14</volume>
<page-range>436</page-range></nlm-citation>
</ref>
<ref id="B14">
<label>14</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lucas]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Asset prices in an exchange economy]]></article-title>
<source><![CDATA[Econometrika]]></source>
<year>1978</year>
<volume>46</volume>
<page-range>1429</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>15</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hurst]]></surname>
<given-names><![CDATA[H. E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Long-Term Storage Capacity of Reservoirs]]></article-title>
<source><![CDATA[Transactions of the American Society of Civil Engineers]]></source>
<year>1951</year>
<volume>116</volume>
<page-range>770</page-range></nlm-citation>
</ref>
<ref id="B16">
<label>16</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mandelbrot]]></surname>
<given-names><![CDATA[B. B.]]></given-names>
</name>
<name>
<surname><![CDATA[Wallis]]></surname>
<given-names><![CDATA[J. R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Robustness of the rescaled range R/S in the measurement of noncyclic long run statistical dependence]]></article-title>
<source><![CDATA[Water Resources Research]]></source>
<year>1969</year>
<volume>5</volume>
<page-range>967</page-range></nlm-citation>
</ref>
<ref id="B17">
<label>17</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wang]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Antar]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Devynck]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Hurst exponent and longtime correlation]]></article-title>
<source><![CDATA[Physics of Plasmas]]></source>
<year>2000</year>
<volume>7</volume>
<page-range>1181</page-range></nlm-citation>
</ref>
<ref id="B18">
<label>18</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Li]]></surname>
<given-names><![CDATA[C.-F.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Rescaled-range and power spectrum analyses on welllogging data]]></article-title>
<source><![CDATA[Geophysical Journal International]]></source>
<year>2003</year>
<volume>153</volume>
<page-range>201</page-range></nlm-citation>
</ref>
<ref id="B19">
<label>19</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sánchez]]></surname>
<given-names><![CDATA[M. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Trinidad]]></surname>
<given-names><![CDATA[J. E.]]></given-names>
</name>
<name>
<surname><![CDATA[García]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Fernández]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Effect of the Underlying Distribution in Hurst Exponent Estimation]]></article-title>
<source><![CDATA[PLoS ONE]]></source>
<year>2015</year>
<volume>10</volume>
</nlm-citation>
</ref>
<ref id="B20">
<label>20</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lo]]></surname>
<given-names><![CDATA[A. W.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Long-Term Memory in Stock Market Prices]]></article-title>
<source><![CDATA[Econometrica]]></source>
<year>1991</year>
<volume>59</volume>
<page-range>1279</page-range></nlm-citation>
</ref>
<ref id="B21">
<label>21</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Willinger]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
<name>
<surname><![CDATA[Taqqu]]></surname>
<given-names><![CDATA[M. S.]]></given-names>
</name>
<name>
<surname><![CDATA[Teverovsky]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Stock market prices and long-range dependence]]></article-title>
<source><![CDATA[Finance Stochast]]></source>
<year>1999</year>
<volume>3</volume>
<page-range>1</page-range></nlm-citation>
</ref>
<ref id="B22">
<label>22</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Barunik]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Kristoufek]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On Hurst exponent estimation under heavy-tailed distributions]]></article-title>
<source><![CDATA[Physica A: Statistical Mechanics and its Applications]]></source>
<year>2010</year>
<volume>389</volume>
<page-range>3844</page-range></nlm-citation>
</ref>
<ref id="B23">
<label>23</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cajueiro]]></surname>
<given-names><![CDATA[D. O.]]></given-names>
</name>
<name>
<surname><![CDATA[Tabak]]></surname>
<given-names><![CDATA[B. M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Hurst exponent over time: testing the assertion that emerging markets are becoming more effcient]]></article-title>
<source><![CDATA[Physica A: Statistical Mechanics and its Applications]]></source>
<year>2004</year>
<volume>336</volume>
<page-range>521</page-range></nlm-citation>
</ref>
<ref id="B24">
<label>24</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Eom]]></surname>
<given-names><![CDATA[Ch.]]></given-names>
</name>
<name>
<surname><![CDATA[Choi]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Oh]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Jung]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Hurst exponent and prediction based on weak-form efficient market hypothesis of stock markets]]></article-title>
<source><![CDATA[Physica A: Statistical Mechanics and its Applications]]></source>
<year>2008</year>
<volume>387</volume>
<page-range>4630</page-range></nlm-citation>
</ref>
<ref id="B25">
<label>25</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Grech]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Mazur]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Can one make any crash prediction in finance using the local Hurst exponent idea?]]></article-title>
<source><![CDATA[Physica A: Statistical Mechanics and its Applications]]></source>
<year>2004</year>
<volume>336</volume>
<page-range>133</page-range></nlm-citation>
</ref>
<ref id="B26">
<label>26</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Peters]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Fractal Market Analysis. Applying Chaos Theory to Investment and Economics]]></source>
<year>1994</year>
<page-range>39-85</page-range><publisher-loc><![CDATA[New York ]]></publisher-loc>
<publisher-name><![CDATA[John Wiley and Sons, INC]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B27">
<label>27</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sánchez]]></surname>
<given-names><![CDATA[M.A.]]></given-names>
</name>
<name>
<surname><![CDATA[Trinidad]]></surname>
<given-names><![CDATA[J.E.]]></given-names>
</name>
<name>
<surname><![CDATA[García]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[García]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Some comments on Hurst exponent and the long memory processes on capital markets]]></article-title>
<source><![CDATA[Physica A: Statistical Mechanics and its Applications]]></source>
<year>2008</year>
<volume>387</volume>
<page-range>5543</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
