Gaussian kernel GARCH models
This paper aims to investigate a Bayesian sampling approach to parameter estimation in the GARCH model with an unknown conditional error density, which we approximate by a mixture of Gaussian densities centered at individual errors and scaled by a common standard deviation. This mixture density has the form of a kernel density estimator of the errors with its bandwidth being the standard deviation. This study is motivated by the lack of robustness in GARCH models with a parametric assumption for the error density when used for error-density based inference such as value-at-risk (VaR) estimation. A contribution of the paper is to construct the likelihood and posterior of the model and bandwidth parameters under the kernel-form error density, and to derive the one-step-ahead posterior predictive density of asset returns. We also investigate the use and benefit of localized bandwidths in the kernel-form error density. A Monte Carlo simulation study reveals that the robustness of the kernel-form error density compensates for the loss of accuracy when using this density. Applying this GARCH model to daily return series of 42 assets in stock, commodity and currency markets, we find that this GARCH model is favored against the GARCH model with a skewed Student t error density for all stock indices, two out of 11 currencies and nearly half of the commodities. This provides an empirical justification for the value of the proposed GARCH model.
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- Hansen, Bruce E, 1994.
"Autoregressive Conditional Density Estimation,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-30, August.
- Tom Doan, . "RATS programs to replicate Hansen's GARCH models with time-varying t-densities," Statistical Software Components RTZ00086, Boston College Department of Economics.
- Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
- Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993.
" On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks,"
Journal of Finance,
American Finance Association, vol. 48(5), pages 1779-1801, December.
- Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
- Koop, Gary, 1994. "Bayesian Semi-nonparametric ARCH Models," The Review of Economics and Statistics, MIT Press, vol. 76(1), pages 176-81, February.
- Zhang, Xibin & King, Maxwell L. & Hyndman, Rob J., 2006. "A Bayesian approach to bandwidth selection for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3009-3031, July.
- Linton, Oliver, 1993.
"Adaptive Estimation in ARCH Models,"
Cambridge University Press, vol. 9(04), pages 539-569, August.
- John Geweke, 1999.
"Using simulation methods for bayesian econometric models: inference, development,and communication,"
Taylor & Francis Journals, vol. 18(1), pages 1-73.
- John Geweke, 1998. "Using simulation methods for Bayesian econometric models: inference, development, and communication," Staff Report 249, Federal Reserve Bank of Minneapolis.
- Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998.
"Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models,"
Review of Economic Studies,
Wiley Blackwell, vol. 65(3), pages 361-93, July.
- Tom Doan, . "RATS programs to replicate Jacquier, Polson, Rossi (1994) stochastic volatility," Statistical Software Components RTZ00105, Boston College Department of Economics.
- Tom Doan, . "KSCPOSTDRAW: RATS procedure to draw from posterior density needed in stochastic volatility model," Statistical Software Components RTS00101, Boston College Department of Economics.
- Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
- Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford.
- Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996. "Stochastic Volatility: Likelihood Inference And Comparison With Arch Models," Econometrics 9610002, EconWPA.
- BAUWENs, Luc & LUBRANO , Michel, 1996.
"Bayesian Inference on GARCH Models using the Gibbs Sampler,"
CORE Discussion Papers
1996027, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Luc Bauwens & Michel Lubrano, 1998. "Bayesian inference on GARCH models using the Gibbs sampler," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages C23-C46.
- Bauwens, L. & Lubrano, M., . "Bayesian inference on GARCH models using the Gibbs sampler," CORE Discussion Papers RP -1307, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Bauwens, L. & Lubrano, M., 1996. "Bayesian Inference on GARCH Models Using the Gibbs Sampler," G.R.E.Q.A.M. 96a21, Universite Aix-Marseille III.
- Jianing Di & Ashis Gangopadhyay, 2011. "On the efficiency of a semi‐parametric GARCH model," Econometrics Journal, Royal Economic Society, vol. 14(2), pages 257-277, 07.
- Xibin Zhang & Maxwell L. King, 2004.
"Box-Cox Stochastic Volatility Models with Heavy-Tails and Correlated Errors,"
Monash Econometrics and Business Statistics Working Papers
26/04, Monash University, Department of Econometrics and Business Statistics.
- Zhang, Xibin & King, Maxwell L., 2008. "Box-Cox stochastic volatility models with heavy-tails and correlated errors," Journal of Empirical Finance, Elsevier, vol. 15(3), pages 549-566, June.
- Singleton, J. Clay & Wingender, John, 1986. "Skewness Persistence in Common Stock Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(03), pages 335-341, September.
- Vrontos, I D & Dellaportas, P & Politis, D N, 2000. "Full Bayesian Inference for GARCH and EGARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 187-98, April.
- Carlo Grillenzoni, 2009. "Kernel Likelihood Inference for Time Series," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 127-140.
- Drost, F.C. & Klaassen, C.A.J., 1996.
"Efficient Estimation in Semiparametric GARCH Models,"
1996-38, Tilburg University, Center for Economic Research.
- Drost, Feike C. & Klaassen, Chris A. J., 1997. "Efficient estimation in semiparametric GARCH models," Journal of Econometrics, Elsevier, vol. 81(1), pages 193-221, November.
- Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Badrinath, S G & Chatterjee, Sangit, 1988. "On Measuring Skewness and Elongation in Common Stock Return Distributions: The Case of the Market Index," The Journal of Business, University of Chicago Press, vol. 61(4), pages 451-72, October.
- Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
- Kanti V. Mardia & John T. Kent & Gareth Hughes & Charles C. Taylor, 2009. "Maximum likelihood estimation using composite likelihoods for closed exponential families," Biometrika, Biometrika Trust, vol. 96(4), pages 975-982.
- Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-59, October.
- Concepción Ausín & Pedro Galeano & Pulak Ghosh, 2010.
"A semiparametric Bayesian approach to the analysis of financial time series with applications to value at risk estimation,"
Statistics and Econometrics Working Papers
ws103822, Universidad Carlos III, Departamento de Estadística y Econometría.
- Ausín, M. Concepción & Galeano, Pedro & Ghosh, Pulak, 2014. "A semiparametric Bayesian approach to the analysis of financial time series with applications to value at risk estimation," European Journal of Operational Research, Elsevier, vol. 232(2), pages 350-358.
- Ao Yuan & Jan G. De Gooijer, 2007. "Semiparametric Regression with Kernel Error Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 841-869.
- Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
- Nakatsuma, Teruo, 2000. "Bayesian analysis of ARMA-GARCH models: A Markov chain sampling approach," Journal of Econometrics, Elsevier, vol. 95(1), pages 57-69, March.
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