Fitting stochastic volatility models in the presence of irregular sampling via particle methods and the em algorithm

Journal of Time Series Analysis

Volumn 29, Issue 5, 2008, Pages 811-833

  Kim, Jeongeun ^b   Stoffer, David S ^a  

^a UNIVERSITY OF PITTSBURGH   (United States)

^b UNIVERSITY OF MARYLAND   (United States)

Author keywords

EM algorithm; Financial time series; Missing data; Mixtures of normals; Particle filtering; Particle smoothing; State space model; Stochastic volatility

Indexed keywords

EID: 49549094501     PISSN: 01439782     EISSN: 14679892     Source Type: Journal    
DOI: 10.1111/j.1467-9892.2008.00584.x     Document Type: Article

References (30)

1. Anderson, W. N., Kleindorfer, G. B., Kleindorfer, P. R. Woodroofe, M. B. (1969) Consistent estimates of the parameters of a linear system. The Annals of Mathematical Statistics 40, 2064 75.
2. Arulampalam, M. S., Maskell S., Gordon, N. Clapp, T. (2002) A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing 50, 174 87.
3. Bai, X., Russell, J. R. Tiao, G. C. (2003) Kurtosis of GARCH and Stochastic Volatility Models with Non-normal Innovations. Journal of Econometrics 114, 349 60.
4. Chan K. S. Ledolter, J. (1995) Monte Carlo EM estimation for time series models involving counts. Journal of the American Statistical Association 90, 242 52.
5. Chib, S., Nardari, F. Shephard, N. (2002) Markov chain Monte Carlo methods for stochastic volatility models. Journal of Econometrics 108, 281 316.
6. Danielson, J. (1994) Stochastic volatility in asset prices: estimation with simulated maximum likelihood. Journal of Econometrics 61, 375 400.
7. Doucet, A. Tadic, B. B. (2003) Parameter estimation in general state-space models using particle methods. Annals of Institute of Statistical Mathematics 55, 409 22.
8. Doucet, A., de Freitas, N. Gordon, N. (2001) Sequential Monte Carlo Methods in Practice. New York : Springer.
9. Durbin, J. Koopman, S. J. (2000) Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives. Journal of the Royal Statistical Society, Series B, 62 : 3 56.
10. Durham, G. B. (2007) SV mixture models with application to s&p 500 index returns. Journal of Financial Economics 85, 822 56.
11. Everitt, B. S. Hand, D. J. (1981) Finite Mixture Distributions. New York : Chapman and Hall.
12. Franses, P. H. van Dijk, D. (2000) Nonlinear Time Series Models in Empirical Finance. New York : Cambridge University Press.
13. Godsill, S., Doucet, A. West, M. (2004) Monte Carlo smoothing for non-linear time series. Journal of the American Statistical Association 199, 156 68.
14. Harvey, A. C., Ruiz, E. Shephard, N. (1994) Multivariate stochastic variance models. Review of Economic Studies 61, 247 64.
15. Hathaway, R. J. (1985) A constrained formulation of maximum-likelihood estimation for normal mixture distributions. The Annals of Statistics 13, 795 800.
16. Jacquier, E., Polson, N. G. Rossi, P. E. (1994) Bayesian analysis of stochastic volatility models. Journal of Business and Economic Statistics 12, 371 417.
17. Kim, J. (2005) Parameter Estimation in Stochastic Volatility Models with Missing Data Using Particle Methods and the EM Algorithm. PhD thesis. University of Pittsburgh, Pittsburgh, PA.
18. Kim, S., Shephard, N. Chib, S. (1998) Stochastic volatility: likelihood inference and comparison with ARCH models. The Review of Economic Studies 65, 361 93.
19. Kitagawa, G. (1996) Monte Carlo filter and smoother for non-Gaussian nonlinear state-space models. Journal of Computational and Graphical Statistics 5, 1 25.
20. Kitagawa, G. Sato, S. (2001) Monte Carlo smoothing and self-organising state-space model. In Sequential Monte Carlo Methods in Practice (eds A. Doucet, N. de Freitas N. Gordon). New York : Springer-Verlag, pp. 177 95.
21. Liesenfeld, R. Richard, J.-F. (2003) Univariate and multivariate stochastic volatility models: estimation and diagnostics. Journal of Empirical Finance, 10, 505 31.
22. Louis, T. A. (1982) Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B 44, 226 33.
23. Mclachlan, G. J. Krishnan, T. (1997) The EM Algorithm and Extensions. New York : John Wiley and Sons, Inc.
24. Mellino, A. Turnbull, S. (1990) Pricing foreign currency options with stochastic volatility. Journal of Econometrics 45, 7 39.
25. Sandmann, G. Koopman, S. (1998) Estimation of stochastic volatility models via monte carlo maximum likelihood. Journal of Econometrics 87, 271 301.
26. Shephard, N. (1996) Statistical aspects of ARCH and stochastic volatility. In Time Series Models: In Econometrics, Finance and Other Fields (eds D. R. Cox, D. V. Hinkley O. E. Barndorff-Nielsen). London : Chapman and Hall, pp. 1 67.
27. Shumway, R. H. Stoffer, D. S. (2006) Time Series Analysis and its Applications: With R Examples. New York : Springer.
28. Stoffer, D. Wall, K. (2004) Resampling in state space models. In State Space and Unobserved Component Models: Theory and Applications (eds A. Harvey, S. J. Koopman, N. Shephard). Cambridge : Cambridge University Press, pp. 171 202.
29. Tanner, M. A. (1996) Tools for Statistical Inference. New York : Springer.
30. Taylor, S. J. (1982) Financial returns modelled by the product of two stochastic processes-a study of daily sugar prices, 1961-79. In Time Series Analysis: theory and Practice, Volume 1 (ed. O. D. Anderson). New York : Elsevier Science Publishing Co., Amsterdam : North-Holland Publishing Co., pp. 203 26.