Publication: ESTUDIO DE LAS CARACTERÍSTICAS MULTIFRACTALES EN LA CORRELACIÓN ENTRE ÍNDICES BURSÁTILES LATINOAMERICANOS Y EL PRECIO DEL CRUDO
Date
2017
Authors
GAJARDO CEA, GABRIEL ENRIQUE
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Abstract
En este tesis se realiza un amplio análisis de las bondades del uso de la teoría fractalen el área financiera. El objetivo es demostrar las limitaciones de las técnicas y supuestoslineales clásicos y superar parcialmente estas limitaciones mediante el uso de técnicasasociadas a la geometría fractal desarrollada por Benoit Mandelbrot.Para este objetivo se realiza una extensiva introducción a la geometría fractal, las ventajasque representa la introducción de dimensiones fraccionales en el análisis y como estepuede ser extendida para el análisis de una propiedad llamada dependencia de largo plazo,cuya interpretación más extendida es la de decaimiento de la función de autocorrelación,o correlación cruzada, de forma más lenta que la asumida exponencial. Esto posee unaserie de implicancias en la dependencia de las series en si mismas y en otras ante pequeñoscambios, los cuales pueden poseer gran influencia en períodos posteriores.Con ello en mente, se cuestionan los fundamentos clásicos de la Hipótesis del MercadoEficiente y se plantean las características de la Hipótesis del Mercado Fractal que aportanrealismo al análisis de series de precios. Se repasan una serie de métodos de estimaciónde las características de dependencia de largo plazo presentes en las series, con las cualeses posible aplicar métricas de eficiencia de mercado, abordándolas desde una perspectivamonofractal. El supuesto de monofractalidad es posteriormente cuestionado ante el aumentode las bondades del análisis fractal cuando se considera un sistema multifractal. Esto esextendido desde el marco de trabajo de la autocorrelación hacia su utilización en el estudiode las correlación cruzada.Además, se realiza una amplia introducción al análisis de los procesos estocásticos y suscaracterísticas. Se introducen además los modelos clásicos utilizados para la descripción deseries financieras y como éstos han sido ampliamente estudiados para la caracterización delas series reales de precios.Finalmente se realiza un repaso de los principales modelos econométricos para el modelamientode series temporales, que si bien presentan gran utilidad en el estudio de las seriesreales, poseen supuestos poco realistas.Con el objetivo de poner estos conocimientos en práctica, se analizan las autocorrelaciones e índices de eficiencia de mercado de seis índices Latinoamericanos y dos de EstadosUnidos, utilizando el método Multifractal Detrended Fluctuation Analysis (MF-DFA).Luego de ello se investiga la correlación entre los índices en cuestión con el precio del crudodado por la corriente del West Texas Intermediate (WTI), utilizando el método llamadoMultifractal Detrended Cross-Correlation Analysis (MF-DCCA).Con el objetivo de extender el análisis y ahondar en las características de la correlación, seanaliza la presencia de asimetría en la correlación cruzada, mediante el estudio del MultifractalDetrended Asymmetric Cross-Correlation Analysis (MF-ADCCA), que permitedemostrar que la correlación cambia según la tendencia de cada serie.El set de datos utilizados cubre el período comprendido entre el 28 de Febrero de 2005y el 29 de Diciembre de 2016, con lo cual es posible observar como la crisis subprimede 2008 influyó en las características de la correlación y autocorrelación. Los resultadosindican un aumento en la ineficiencia de mercado luego de la crisis para la mayoría depaíses Latinoamericanos. Además se encuentra evidencia de correlación con dependenciade largo plazo para todos los índices, junto con altos grados de multifractalidad en ellas.Para analizar la asimetría se consideran por separado las tendencias de cada serie, siendoéstas de vital relevancia en el grado de correlación.Finalmente, mediante el uso de ventana móvil, se examinó el cambio temporal de losexponentes de autocorrelación y de correlación cruzada y sus cambios según tendencia delas series, tanto para el caso clásico, y al considerar la asimetría, encontrándose interesantespatrones en su comportamiento.
In this thesis a broad analysis of the benefits of the use of fractal theory in the financialarea is carried out. The objective is to demonstrate the limitations of classical linear techniquesand assumptions, while partially overcoming these limitations by using techniquesassociated with fractal geometry developed by Benoit Mandelbrot.For this purpose wea present an extensive introduction to the fractal geometry, and analyzethe advantages of the use of fractional dimensions. We also show how this can be extendedfor the analysis of a property called long-term dependency, whose more popular interpretationis as a rate of decay of the autocorrelation function, or cross-correlation, slower thanthe assumed exponential. This has several implications in the dependence of the series onthemselves and in others to small changes, which can have great influence in later periods.With this in mind, the classic foundations of the Ecient Market Hypothesis are questionedand the characteristics of the Fractal Market Hypothesis are presented, which bring realismto the analysis of price series. We review a series of methods for estimating the long-termdependency characteristics present in the series, with which it is possible to apply marketeciency metrics, addressing them from a monofractal perspective. The assumption ofmonofractality is later questioned in light of the increase in the goodness of fractal analysiswhen considering a multifractal system. This is extended from the framework of autocorrelationto its use in the study of cross-correlation.In addition, a broad introduction is made to the analysis of stochastic processes and theircharacteristics. We also introduce the classic models used for the description of financialseries and how they have been extensively studied for the acquisition of characteristics ofthe real series of prices. Finally, a review of the main econometric models for the modelingof time series is carried out, which, while very useful in the study of the real series, haveunrealistic assumptions.In order to put this knowledge into practice, the autocorrelations and market eciencyindices of six Latin American and two US indices are analyzed using the MultifractalDetrended Fluctuation Analysis (MF-DFA) method. After that, the correlation between theindices in question and the West Texas Intermediate (WTI) crude oil price is investigated, using the method called Multifractal Detrended Cross-Correlation Analysis (MF-DCCA).With the aim of extending the analysis and delving into the characteristics of the correlation,we analyze the presence of asymmetry in cross-correlations, by studying the MultifractalDetrended Asymmetric Cross-Correlation Analysis (MF-ADCCA), which allows to demonstratethat the correlation changes according to the trend of each series.The data set used covers the period from February 28, 2005 to December 29, 2016, makingit possible to observe how the subprime crisis of 2008 influenced the characteristics ofcorrelations and autocorrelations. The results indicate an increase in market ineciencyafter the crisis for most Latin-American countries. There is also evidence of correlation withlong-term dependence for all indices, along with high degrees of multifractality in them. Toanalyze the asymmetry, the trends of each series are considered separately, being these ofvital relevance in the asymmetry of the correlations. By using the rolling window method,it is possible to examine the temporal change of the autocorrelation and cross-correlationexponents, under the normal case, and when considering the asymmetry, which allowed tofind interesting patterns in its behavior.
In this thesis a broad analysis of the benefits of the use of fractal theory in the financialarea is carried out. The objective is to demonstrate the limitations of classical linear techniquesand assumptions, while partially overcoming these limitations by using techniquesassociated with fractal geometry developed by Benoit Mandelbrot.For this purpose wea present an extensive introduction to the fractal geometry, and analyzethe advantages of the use of fractional dimensions. We also show how this can be extendedfor the analysis of a property called long-term dependency, whose more popular interpretationis as a rate of decay of the autocorrelation function, or cross-correlation, slower thanthe assumed exponential. This has several implications in the dependence of the series onthemselves and in others to small changes, which can have great influence in later periods.With this in mind, the classic foundations of the Ecient Market Hypothesis are questionedand the characteristics of the Fractal Market Hypothesis are presented, which bring realismto the analysis of price series. We review a series of methods for estimating the long-termdependency characteristics present in the series, with which it is possible to apply marketeciency metrics, addressing them from a monofractal perspective. The assumption ofmonofractality is later questioned in light of the increase in the goodness of fractal analysiswhen considering a multifractal system. This is extended from the framework of autocorrelationto its use in the study of cross-correlation.In addition, a broad introduction is made to the analysis of stochastic processes and theircharacteristics. We also introduce the classic models used for the description of financialseries and how they have been extensively studied for the acquisition of characteristics ofthe real series of prices. Finally, a review of the main econometric models for the modelingof time series is carried out, which, while very useful in the study of the real series, haveunrealistic assumptions.In order to put this knowledge into practice, the autocorrelations and market eciencyindices of six Latin American and two US indices are analyzed using the MultifractalDetrended Fluctuation Analysis (MF-DFA) method. After that, the correlation between theindices in question and the West Texas Intermediate (WTI) crude oil price is investigated, using the method called Multifractal Detrended Cross-Correlation Analysis (MF-DCCA).With the aim of extending the analysis and delving into the characteristics of the correlation,we analyze the presence of asymmetry in cross-correlations, by studying the MultifractalDetrended Asymmetric Cross-Correlation Analysis (MF-ADCCA), which allows to demonstratethat the correlation changes according to the trend of each series.The data set used covers the period from February 28, 2005 to December 29, 2016, makingit possible to observe how the subprime crisis of 2008 influenced the characteristics ofcorrelations and autocorrelations. The results indicate an increase in market ineciencyafter the crisis for most Latin-American countries. There is also evidence of correlation withlong-term dependence for all indices, along with high degrees of multifractality in them. Toanalyze the asymmetry, the trends of each series are considered separately, being these ofvital relevance in the asymmetry of the correlations. By using the rolling window method,it is possible to examine the temporal change of the autocorrelation and cross-correlationexponents, under the normal case, and when considering the asymmetry, which allowed tofind interesting patterns in its behavior.
Description
Catalogado desde la version PDF de la tesis.
Keywords
ANALISIS DE SERIES DE TIEMPO , CORRELACION ASIMETRICA , MERCADO DEL CRUDO , MERCADOS BURSATILES LATINOAMERICANOS , MULTIFRACTALIDAD