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Master's Dissertation
DOI
Document
Author
Full name
David de Souza Dias
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2018
Supervisor
Committee
Ehlers, Ricardo Sandes (President)
Herencia, Mauricio Enrique Zevallos
Moura, Maria Sílvia de Assis
Title in Portuguese
Inferência Bayesiana em Modelos de Volatilidade Estocástica usando Métodos de Monte Carlo Hamiltoniano
Keywords in Portuguese
Inferência Bayesiana
LOO
Método HMC
Modelos de volatilidade estocástica
Valor em Risco (VaR)
WAIC
Abstract in Portuguese
Este trabalho apresenta um estudo através da abordagem Bayesiana em modelos de volatilidade estocástica, para modelagem de séries temporais financeiras, com o uso do método de Monte Carlo Hamiltoniano (HMC). Propomos o uso de outras distribuições para os erros da equação de observações do modelos de volatilidade estocástica, além da distribuição Gaussiana, para tratar problemas como caudas pesadas e assimetria nos retornos. Além disso, utilizamos critérios de informações, recentemente desenvolvidos, WAIC e LOO que aproximam a metodologia de validação cruzada, para realizar a seleção de modelos. No decorrer do trabalho, estudamos a qualidade do método HMC através de exemplos, estudo de simulação e aplicação a conjunto de dados. Adicionalmente, avaliamos a performance dos modelos e métodos propostos através do cálculo de estimativas para o Valor em Risco (VaR) para múltiplos horizontes de tempo.
Title in English
Bayesian Inference in Stochastic Volatility Models using Hamiltonian Monte Carlo Methods
Keywords in English
Bayesian inference
HMC methods
LOO
Stochastic volatility models
Value at Risk (VaR)
WAIC
Abstract in English
This paper presents a study using Bayesian approach in stochastic volatility models for modeling financial time series, using Hamiltonian Monte Carlo methods (HMC). We propose the use of other distributions for the errors of the equation at stochastic volatiliy model, besides the Gaussian distribution, to treat the problem as heavy tails and asymmetry in the returns. Moreover, we use recently developed information criteria WAIC and LOO that approximate the crossvalidation methodology, to perform the selection of models. Throughout this work, we study the quality of the HMC methods through examples, simulation study and application to dataset. In addition, we evaluated the performance of the proposed models and methods by calculating estimates for Value at Risk (VaR) for multiple time horizons.
 
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Publishing Date
2019-07-17
 
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