Abstract
Jacquier, Poison and Rossi (1994, Journal of Business and Economic Statistics) have proposed a Bayesian hierarchical model and Markov Chain Monte Carlo methodology for parameter estimation and smoothing in a stochastic volatility model, where the logarithm of the conditional variance follows an autoregressive process. In sampling experiments, their estimators perform particularly well relative to a quasi-maximum likelihood approach, in which the nonlinear stochastic volatility model is linearized via a logarithmic transformation and the resulting linear state-space model is treated as Gaussian. In this paper, we explore a simple modification to the treatment of inlier observations which reduces the excess kurtosis in the distribution of the observation disturbances and improves the performance of the quasi-maximum likelihood procedure. The method we propose can be carried out with commercial software.
This is a preview of subscription content, log in via an institution to check access.
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
Abramowitz, M and Stegun, IA (1965).Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series 55
Andersen, T.G. (1994). Comment on Jacquier, Poison and Rossi’s “Bayesian analysis of stochastic volatility models”.Journal of Business and Economic Statistics12, 389–392
Andersen, T.G. and S0rensen, B. (1994). Estimation of a stochastic volatility model: a Monte Carlo study. Working paper, Northwestern University, J.L. Kellogg Graduate School of Management.
Bartlett, M.S. and Kendall, D.G. (1946). The statistical analysis of variance—heterogeneity and the logarithmic transformation. Supplement to theJournal of the Royal Statistical Society, Vol. VIII, 128–133
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity,Journal of Econometrics31, 307–327
Bollerslev, T., Chou, R.Y., and Kroner, K.F. (1992). ARCH modeling in finance,Journal of Econometrics52, 5–59
Brockwell, P.J. and Davis, R.A. (1991).Time Series: Theory and Methods, 2nd ed., Springer- Verlag, New York
Carter, C.K. (1993). On Markov chain Monte Carlo methods for linear state space modelling.Unpublished Ph.D. dissertation University of New South Wales
Clark, P.K. (1973). A subordinated stochastic process model with finite variances for speculative prices,Econometrica41, 135–156
Engle, R.F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation.Econometrica50, 987–1007
Fuller, W.A. (forthcoming).Introduction to Statistical Time Series 2nd ed., John Wiley, New York
Harvey, A.C. (1989).Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge University Press, Cambridge
Harvey, AC, and Shephard, N (1993). Estimation and testing of stochastic variance models.Unpublished manuscript, The London School of Economics
Harvey, A.C., Ruiz, E., and Shephard, N. (1994). Multivariate stochastic variance models,Review of Economic Studies61, 247–264
Hull, J., and White, A. (1987). The pricing of options on assets with stochastic volatilities.Journal of Finance42, 281–300
Jacquier, E., Poison, N.G. and Rossi, P.E. (1994). Bayesian analysis of stochastic volatility models (with discussion).Journal of Business and Economic Statistics12, 371–417
Kim, S., and Shephard, N. (1994). Stochastic volatility: likelihood inference and comparison with ARCH models.Unpublished working paper, Nuffield College, Oxford
Mahieu, R. and Schotman, P. (1994). Stochastic volatility and the distribution of exchange rate news. Discussion Paper 96, Institute for Empirical Macroeconomics, Federal Reserve Bank of Minneapolis
Melino, A. and and Turnbull, S.M. (1990). Pricing foreign currency options with stochastic volatility.Journal of Econometrics45, 239–265
Nelson, D.B. (1988). Time series behavior of stock market volatility and returns.Unpublished PhD dissertation, Massachusetts Institute of Technology, Economics Department
Nelson, D.B. (1994). Comment on Jacquier, Poison and Rossi’s “Bayesian analysis of stochastic volatility models”.Journal of Business and Economic Statistics12, 403–406
Ruiz, E. (1994). Quasi-maximum likelihood estimation of stochastic volatility models.Journal of Econometrics63, 289–306
Shephard, N. (1994). Partial non-Gaussian state space.Biometrika81, 115–131
Tauchen, G., and Pitts, M. (1983). The price variability-volume relationship on speculative markets.Econometrica51, 485–505
Taylor, S. (1986).Modelling Financial Time Series, Wiley, New York
Vetzal, K. (1992). Stochastic short rate volatility and the pricing of bonds and bond options.Unpublished PhD dissertation, University of Toronto, Department of Economics
Wishart, J. (1947). The cumulants of the z and of the logarithmicx 2andtdistributions.Biometrika34, 170–178
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media New York
About this chapter
Cite this chapter
Breidt, F.J., Carriquiry, A.L. (1996). Improved Quasi-Maximum Likelihood Estimation for Stochastic Volatility Models. In: Lee, J.C., Johnson, W.O., Zellner, A. (eds) Modelling and Prediction Honoring Seymour Geisser. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2414-3_14
Download citation
DOI: https://doi.org/10.1007/978-1-4612-2414-3_14
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7529-9
Online ISBN: 978-1-4612-2414-3
eBook Packages: Springer Book Archive