Estimación adaptativa de la volatilidad en una serie de tiempo financiera.
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Date
2022
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Journal ISSN
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Publisher
Universidad de Concepción
Abstract
El presente trabajo de tesis de Magíster en Estadística de la Universidad de Concepción tiene como objetivo proponer una nueva forma de modelar y predecir la volatilidad multivariada. Está sustentado en la importancia para el mundo de las finanzas, debido a la fuerte relación entre volatilidad, rendimiento y riesgo de una inversión.
Los métodos paramétricos clásicos aunque muy utilizados en muchas ocasiones no son adecuados, ya que en su formulación contienen restricciones que a menudo son violadas por los datos empíricos. El modelo propuesto, utiliza como metodología el procedimiento adaptativo local de punto de cambio, donde el estimador se va adaptando a los datos, mediante el uso de la Divergencia de Kullback-Leibler. Se definen todos los conceptos necesarios para validar el uso del Estimador, Propiedades del Estimador, Condiciones de Propagación, Calidad de la Estimación mediante Desigualdades de Oráculo, Estabilidad, etc.
Esta investigación no solo es teórica, también se aplica a Datos Reales de Tipo de Cambio de Divisas y se compara con técnicas clásicas, los modelos de Correlación Dinámica Condicional, donde se demostró que el modelo adaptativo fue muy superior, sobretodo en dos aspectos, tiempo invertido en la predicción y calidad de la estimación, donde resalta el horizonte de tiempo de 1 día con el 97; 54% de los casos favorables para el estimador adaptativo y a 3 días con el 53; 95% de los casos.
This thesis work of Master in Statistics the University of Concepcion aims to propose a novel method procedure for change point detection estimator adaptative to the data nonparametric statistics. It is based on the importance for the world of finance, due to the strong relationship between volatility, return and risk of an investment. The classical parametric methods, although widely used, are often inadequate, since their formulation contains restrictions that are often violated by the empirical data. The proposed model uses as a methodology the local adaptive procedure of change point, where the estimator is adapted to the data, through the use of the Kullback-Leibler divergence. Properties of the estimator, propagation conditions, estimation quality by means of estimation inequalities, stability, etc., are defined. This research is not only theoretical, it is also applied to Real Foreign Exchange Rate Data and is compared with classical techniques, the Conditional Dynamic Correlation models, where it was demonstrated that the adaptive model was far superior, especially in two aspects, time invested in the prediction and quality of the estimation, where the time horizon of 1 day stands out with 97;54% of the favorable cases for the adaptive estimator and 3 days with 53;95% of the cases.
This thesis work of Master in Statistics the University of Concepcion aims to propose a novel method procedure for change point detection estimator adaptative to the data nonparametric statistics. It is based on the importance for the world of finance, due to the strong relationship between volatility, return and risk of an investment. The classical parametric methods, although widely used, are often inadequate, since their formulation contains restrictions that are often violated by the empirical data. The proposed model uses as a methodology the local adaptive procedure of change point, where the estimator is adapted to the data, through the use of the Kullback-Leibler divergence. Properties of the estimator, propagation conditions, estimation quality by means of estimation inequalities, stability, etc., are defined. This research is not only theoretical, it is also applied to Real Foreign Exchange Rate Data and is compared with classical techniques, the Conditional Dynamic Correlation models, where it was demonstrated that the adaptive model was far superior, especially in two aspects, time invested in the prediction and quality of the estimation, where the time horizon of 1 day stands out with 97;54% of the favorable cases for the adaptive estimator and 3 days with 53;95% of the cases.
Description
Tesis presentada para optar al grado de Magíster en Estadística.
Keywords
Correlación (Estadística), Finanzas