Summary
This paper provides a Bayesian analysis of a semiparametric autoregressive conditional heteroscedasticity (ARCH) model. We propose a semiparametric ARCH model using a Dirichlet process prior and show a Markov chain Monte Carlo method for the posterior inference. The model is estimated with a data set of monthly exchange rate for the Deutsche Mark to the U. S. Dollar.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Antoniak, C.E. (1974): Mixtures of Dirichlet processes with applications to non-parametric problems. The Annals of Statistics 2, 1152–1174
Besag, J. and Green, P.J. (1993): Spatial statistics and Bayesian computation. Journal of the Royal Statistical Society Ser. B 55, 25–37
Blackwell, D. and MacQueen, J.B. (1973): Ferguson distributions via Pólya urn schemes. The Annals of Statistics 1, 353–355
Bollerslev, T., Chou, R.Y., and Kroner, K.F. (1992): ARCH modeling in finance. Journal of Econometrics 52, 5–59
Doss, H. (1994): Bayesian nonparametric estimation for incomplete data via suc-cessive substitution sampling. The Annals of Statistics 22, 1763–1786
Engle, R.F. (1982): Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation. Econometrica 50, 987–1008
Escobar, M.D. (1994): Estimating normal means with a Dirichlet process prior. Journal of the American Statistical Association 89, 268–277
Escobar, M.D. and West, M. (1995): Bayesian density estimation and inference using mixtures. Journal of the American Statistical Association 90, 577–587
Ferguson, T.S. (1973): A Bayesian analysis of some nonparametric problems. The Annals of Statistics 1, 209–230
Gallant, A.R. and Tauchen, G. (1989): Seminonparametric estimation of conditionally constrained heterogeneous processes: Asset pricing applications. Econometrica 57, 1091–1120
Gallant, A.R. and Tauchen, G. (1992): A nonparametric approach to nonlinear time series analysis: Estimation and simulation. In New Directions in Time Series Analysis, eds. D. Brillinger, P. Cames, J. Geweke, E. Parzen, M. Rosenblatt and M. Taqqu, 71–92. New York: Springer—Verlag
Gelfand, A.E. and Smith, A.F.M. (1990): Sampling based approaches to calculate marginal densities. Journal of the American Statistical Association 85, 398–409
Geman, S. and Geman, D. (1984): Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6, 721–741
Geweke, J. (1986): Modeling the persistence of conditional variances: A comment. Econometric Reviews 5, 57–61
Hasting, W.K. (1970): Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97–109
Jacquier, E., Poison, N.G., and Rossi, P.E. (1994): Bayesian analysis of stochastic volatility models (with discussion). Journal of Business and Economic Statistics 12, 371–417
Kuo, L. and Mallick, B.K. (1997): Bayesian semiparametric inference for the accel-erated failure time model. Canadian Journal of Statistics in press.
MacEachern, S.N. and Müller, P. (1994): Estimating mixture of Dirichlet process models. Tech.Rep.94–11, ISDS, Duke University.
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. (1953): Equations of state calculations by fast computing machines. Journal of Chemical Physics 21, 1087–1091
Müller, P., Erkanli, A. and West, M. (1996): Bayesian curve fitting using multivariate normal mixtures. Biometrika 83, 67–79
Pagan, A.R. and Ullah, A. (1988): The econometric analysis of models with risk terms. Journal of Applied Econometrics 3, 87–105
Pantula, S.G. (1986): Modeling the persistence of conditional variances: A comment. Econometric Reviews 5, 71–74
Robinson, P.M. (1987): Asymptotically efficient estimation in the presence of heteroskedasticity of unknown form. Econometrica 55, 875–891
Robinson, P.M. (1988): Semiparametric econometrics: A survey. Journal of Applied Econometrics 4, 35–51
Shephard, N. (1994): Partial non—Gaussian state space. Biometrika 81, 115–131
Smith, A.F.M. and Roberts, G.O. (1993): Bayesian computations via the Gibbs sampler and related Markov chain Monte Carlo methods. Journal of the Royal Statistical Society Ser. B 55, 3–23
Tanner, M.A. and Wong, W.H. (1987): The calculation of posterior distribution by data augmentation (with discussion). Journal of the American Statistical Association 82, 528–550
West, M., Müller, P. and Escobar, M.D. (1994): Hierarchical priors and mixture models, with application in regression and density estimation. In Aspects of Uncertainty: A Tribute to D.V. Lindley, eds. A.F.M. Smith and P. Freeman, 363–385. New York: Wiley
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Kozumi, H., Polasek, W. (2000). A Bayesian Semiparametric Analysis of ARCH Models. In: Dockner, E.J., Hartl, R.F., Luptačik, M., Sorger, G. (eds) Optimization, Dynamics, and Economic Analysis. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57684-3_33
Download citation
DOI: https://doi.org/10.1007/978-3-642-57684-3_33
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-642-63327-0
Online ISBN: 978-3-642-57684-3
eBook Packages: Springer Book Archive