<?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>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332019000100045</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v26i1.35518</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Estimación de modelos de volatilidad estocástica vía filtro auxiliar de partículas]]></article-title>
<article-title xml:lang="en"><![CDATA[Estimation of stochastic volatility models via auxiliary particles filter]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Trosel]]></surname>
<given-names><![CDATA[Yeniree]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Hernández]]></surname>
<given-names><![CDATA[Aracelis]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Infante]]></surname>
<given-names><![CDATA[Saba]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Carabobo Facultad de Ciencia y Tecnología Departamento de Matemáticas]]></institution>
<addr-line><![CDATA[ Valencia]]></addr-line>
<country>Venezuela</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Investigación de Tecnología Experimental Yachay Tech Escuela de Ciencias Matemáticas y Computacionales ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Ecuador</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad de Investigación de Tecnología Experimental Yachay Tech  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Ecuador</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2019</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2019</year>
</pub-date>
<volume>26</volume>
<numero>1</numero>
<fpage>45</fpage>
<lpage>81</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332019000100045&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332019000100045&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332019000100045&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen [16] El creciente interés en el estudio de la volatilidad para series de instru- mentos financieros nos lleva a plantear una metodología basada en la ver- satilidad de los métodos Monte Carlo Secuencial (MCS) para la estimación de los estados del modelo de volatilidad estocástica general (MVEG). En este trabajo se propone una metodología basada en la estructura espacio estado aplicando técnicas de filtrado como es el caso del filtro auxiliar de partículas para la estimación de la volatilidad subyacente del sistema. Adi- cionalmente, se propone utilizar un algoritmo Monte Carlo por cadenas de Markov (MCMC), como es el muestreador de Gibbs para la estimación de los parámetros. La metodología es ilustrada usando una serie de re- tornos de datos simulados, y la serie de retornos correspondiente al índice de precio Standard and Poor&#8217;s 500 (S&amp;P 500) para el periodo 1995 2003. Los resultados evidencian que la metodología propuesta permite explicar adecuadamente la dinámica de la volatilidad cuando existe una respuesta asimétrica de esta ante un shock de diferente signo, concluyendo que los cambios bruscos en los retornos corresponden a valores altos en la volati- lidad.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract [20] The growing interest in the study of volatility for series of financial instruments leads us to propose a methodology based on the versatility of the Sequential Monte Carlo (SMC) methods for the estimation of the states of the general stochastic volatility model (GSVM). In this paper, we pro- posed a methodology based on the state space structure applying filtering techniques such as the auxiliary particles filter for estimating the underly- ing volatility of the system. Additionally, we proposed to use a Markov chain Monte Carlo (MCMC ) algorithm, such as is the Gibbs sampler for the estimation of the parameters. The methodology is illustrated through a series of returns of simulated data, and the series of returns correspond- ing to the Standard and Poor&#8217;s 500 price index (S&amp;P 500) for the period 1995 2003. The results show that the proposed methodology allows to adequately explain the dynamics of volatility when there is an asymmet- ric response of this to a shock of a different sign, concluding that abrupt changes in returns correspond to high values in volatility.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[modelos de volatilidad estocástica]]></kwd>
<kwd lng="es"><![CDATA[modelos espacio estado]]></kwd>
<kwd lng="es"><![CDATA[filtro auxiliar de partículas]]></kwd>
<kwd lng="en"><![CDATA[stochastic volatility models]]></kwd>
<kwd lng="en"><![CDATA[space state models]]></kwd>
<kwd lng="en"><![CDATA[auxiliary particles filter]]></kwd>
</kwd-group>
</article-meta>
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