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A Comparative Study Of Bayesian And Maximum Likelihood Approaches For Arch Models With Evidence From Brazilian Financial Series

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  • MARINHO G. ANDRADE

    (Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de Computação – ICMC, Universidade de São Paulo – USP, Av. do Trabalhador Sãocarlense 400, CEP 13566-590, São Carlos, São Paulo, Brazil)

  • SANDRA C. OLIVEIRA

    (Campus de Tupã, Universidade Estadual Paulista – UNESP, Av. Domingos da Costa Lopes 780, CEP 17602-660, Tupã, São Paulo, Brazil)

Abstract

The purpose of this study is to address the inference problem of the parameters of autoregressive conditional heteroscedasticity (ARCH) models. Specifically, we present a comparison of the two approaches — Bayesian and Maximum Likelihood (ML) for ARCH models, and the specific mathematical and algorithmic formulations of these approaches. In the ML, estimation we obtain confidence intervals by using the Bootstrap simulation technique. In the Bayesian estimation, we present a reparametrization of the model which allows us to apply prior normal densities to the transformed parameters. The posterior estimates are obtained using Monte Carlo Markov Chain (MCMC) methods. The methodology is exemplified by considering two Brazilian financial time series: the Bovespa Stock Index — IBovespa and the Telebrás series. The order of each ARCH model is selected by using the Bayesian Information Criterion (BIC).

Suggested Citation

  • Marinho G. Andrade & Sandra C. Oliveira, 2011. "A Comparative Study Of Bayesian And Maximum Likelihood Approaches For Arch Models With Evidence From Brazilian Financial Series," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 347-361.
    • Handle: RePEc:wsi:nmncxx:v:07:y:2011:i:02:n:s1793005711001974
    DOI: 10.1142/S1793005711001974
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    References listed on IDEAS

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    1. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    2. Pascual, Lorenzo & Romo, Juan & Ruiz Ortega, Esther, 2000. "Forecasting returns and volatilities in GARCH processes using the bootstrap," DES - Working Papers. Statistics and Econometrics. WS 10059, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. repec:wop:ubisop:0001 is not listed on IDEAS
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