Stock index returns’ density prediction using GARCH models: Frequentist or Bayesian estimation?

Ardia, David and Lennart, Hoogerheide and Nienke, Corré (2011): Stock index returns’ density prediction using GARCH models: Frequentist or Bayesian estimation?

Abstract

Using well-known GARCH models for density prediction of daily S&P 500 and Nikkei 225 index returns, a comparison is provided between frequentist and Bayesian estimation. No significant difference is found between the qualities of the forecasts of the whole density, whereas the Bayesian approach exhibits significantly better left-tail forecast accuracy.

• Item Type: MPRA Paper
• Language: English
• Keywords: GARCH; Bayesian; KLIC; censored likelihood
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General

References

Ardia, D., 2008. Financial Risk Management with Bayesian Estimation of GARCH Models: Theory and Applications. Vol. 612 of Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin, Germany.

Ardia, D., Hoogerheide, L. F., 2010. Efficient Bayesian estimation and combination of GARCH-type models. In: Böcker, K. (Ed.), Rethinking Risk Measurement and Reporting - Volume II: Examples and Applications from

Finance. Risk Books, London, Ch. 1.

Bauwens, L., Lubrano, M., 1998. Bayesian inference on GARCH models using the Gibbs sampler. Econometrics Journal 1, C23–C46.

Bollerslev, T., 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31 (3), 307–327.

Diebold, F. X., Mariano, R. S., 1995. Comparing predictive accuracy. Journal of Business & Economic Statistics 13 (3), 253–263.

Diks, C., Panchenko, V., Van Dijk, D., 2008. Partial likelihood-based scoring rules for evaluating density forecasts in tails. Tinbergen Institute Discussion Paper TI 2008-050/4.

Geweke, J., Amisano, G., 2010. Comparing and evaluating Bayesian predictive distributions of asset returns. International Journal of Forecasting 26, 216–230.

Geweke, J. F., 1993. Bayesian treatment of the independent Student-t linear model. Journal of Applied Econometrics 8 (S1), S19–S40.

Glosten, L. R., Jaganathan, R., Runkle, D. E., 1993. On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance 48 (5), 1779–1801.

Hoogerheide, L. F., Kaashoek, J. F., Van Dijk, H. K., 2007. On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: An application of flexible sampling methods using neural networks. Journal of Econometrics 139 (1), 154–180.

Hoogerheide, L. F., Van Dijk, H. K., 2010. Bayesian forecasting of Value at Risk and Expected Shortfall using adaptive importance sampling. International Journal of Forecasting 26, 231–247.

Mitchel, J., Hall, S. G., 2005. Evaluating, comparing and combining density forecasts using the KLIC with an application to the Bank of England and NIESR ‘fan’ charts of inflation. Oxford Bulletin of Economics and Statistics 67, 995–1033.

Nakatsuma, T., Tsurumi, H., 1996. ARMA-GARCH models: Bayes estimation versus MLE, and Bayes non- stationarity test. Working Paper No. 9619, Department of Economics, Rutgers University, New Jersey.

Nelson, D. B., 1991. Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59 (2), 347–370.