MCMC use in Bayesian approach of GARCH models

• Grant number: 98/12750-2
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 1999
• End date: November 30, 2000
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Applied Probability and Statistics
• Principal Investigator: Marinho Gomes de Andrade Filho
• Grantee: Valeria Aparecida Martins Ferreira
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

In this work a sequence of procedures are described to estimate parameters, to select order and to forecast the Autoregressive Conditional Heteroskedasticity ARCH(p) and the generalized ARCH, GARCH(p,q) models. The estimates are obtained by using both classical maximum likelihood method and Bayesian inference approach jointly with simulation of Monte Carlo Markov Chain (MCMC). In the Bayesian analysis we use normal prior densities for the parameters of the model. The methods were applied in a simulated data and in three real sets of data of the Brazilian finance market: Index Bovespa, Telebrás and Quotation in American Dollar of the Japanese Yen. In general, the performance of maximum likelihood and Bayesian estimates are similar. However, in some series, the 95% confidence intervals for some parameters of the model, presented negative values, violating the constraints imposed to the parameters of the ARCH(p) models, highlighting certain advantage of the Bayesian approach. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

FERREIRA, Valeria Aparecida Martins. Uso de MCMC na abordagem Bayesiana de modelos ARCH e GARCH. 2001. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.