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Bayesian Estimation Of The Parameters Of The Arch Model With Normal Innovations Using Lindley’S Approximation

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  • Yakup ARI

    (Department of Mathematics, Yeditepe University, Istanbul, Turkey)

  • Alexandros PAPADOPOULOS

    (Department of Mathematics,Yeditepe University, Istanbul, Turkey)

Abstract

Autoregressive conditionally heteroscedastic (ARCH) models are used to analyze empirical financial data and capture various stylized facts in financial econometrics. The procedure that is most commonly used for estimating the unknown parameters of an ARCH model is the maximum likelihood estimation (MLE). In this study, it is assumed that the parameters of the ARCH model are random variables having known prior probability density functions, and therefore they will be estimated using Bayesian methods. The Bayesian estimators are not in a closed form, and thus Lindley’s approximation will be used to estimate them. The Bayesian estimators are derived under squared error loss (SEL) and linear exponential (LINEX) loss functions. An example is given in order to illustrate the findings and furthermore, Monte Carlo simulations are performed in order to compare the ML estimates to the Bayesian ones. Finally, conclusions on the findings are given.

Suggested Citation

  • Yakup ARI & Alexandros PAPADOPOULOS, 2016. "Bayesian Estimation Of The Parameters Of The Arch Model With Normal Innovations Using Lindley’S Approximation," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(4), pages 217-234.
    • Handle: RePEc:cys:ecocyb:v:50:y:2016:i:4:p:217-234
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    References listed on IDEAS

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    1. West, Kenneth D. & Edison, Hali J. & Cho, Dongchul, 1993. "A utility-based comparison of some models of exchange rate volatility," Journal of International Economics, Elsevier, vol. 35(1-2), pages 23-45, August.
    2. Christoffersen, Peter F. & Diebold, Francis X., 1997. "Optimal Prediction Under Asymmetric Loss," Econometric Theory, Cambridge University Press, vol. 13(6), pages 808-817, December.
    3. Nobay, A. Robert & Peel, David, 1998. "Optimal monetary policy in a model of asymmetric central bank preferences," LSE Research Online Documents on Economics 119138, London School of Economics and Political Science, LSE Library.
    4. Arup Bose & Kanchan Mukherjee, 2003. "Estimating The Arch Parameters By Solving Linear Equations," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(2), pages 127-136, March.
    5. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    6. Batchelor, Roy & Peel, David A., 1998. "Rationality testing under asymmetric loss," Economics Letters, Elsevier, vol. 61(1), pages 49-54, October.
    7. W. R. Gilks & N. G. Best & K. K. C. Tan, 1995. "Adaptive Rejection Metropolis Sampling Within Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(4), pages 455-472, December.
    8. Granger, C. W. J. & Newbold, Paul, 1986. "Forecasting Economic Time Series," Elsevier Monographs, Elsevier, edition 2, number 9780122951831 edited by Shell, Karl.
    9. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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