Likelihood analysis of non-Gaussian measurement time series

Biometrika

Volumn 84, Issue 3, 1997, Pages 653-667

  Shephard, Neil ^a   Pitt, Michael K ^b  

^a NUFFIELD COLLEGE   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Blocking; Exponential family; Importance sampling; Markov chain Monte Carlo; Simulation smoother; Stochastic volatility

Indexed keywords

EID: 0003258788     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/84.3.653     Document Type: Article

References (36)

1. CARLIN, B. P., POLSON, N. G. & STOFFER, D. (1992). A Monte Carlo approach to nonnormal and nonlinear state-space modelling. J. Am. Statist. Assoc. 87, 493-500.
2. CARTER, C. K. & KOHN, R. (1994). On Gibbs sampling for state space models. Biometrika 81, 541-53.
3. CARTER, C. K. & KOHN, R. (1996). Markov chain Monte Carlo in conditionally Gaussian state space models. Biometrika 83, 589-601.
4. CHAN, K. S. & LEDOLTER, J. (1995). Monte Carlo EM estimates for time series models involving counts. J. Am. Statist. Assoc. 89, 242-52.
5. CHIB, S. & GREENBERG, E. (1995). Understanding the Metropolis-Hastings algorithm. Am. Statistician 49, 327-35.
6. DANIELSSON, J. & RICHARD, J. F. (1993). Accelerated Gaussian importance sampler with application to dynamic latent variable models. J. Appl. Economet. 8, S153-74.
7. DE JONG, P. (1989). Smoothing and interpolation with the state space model. J. Am. Statist. Assoc. 84, 1085-8.
8. DE JONG, P. & SHEPHARD, N. (1995). The simulation smoother for time series models. Biometrika 82, 339-50.
9. DOORNIK, J. A. (1996). Ox: Object Oriented Matrix Programming, 1.10. London: Chapman and Hall.
10. DURBIN, J. & KOOPMAN, S. J. (1997). Monte Carlo maximum likelihood estimation for non-Gaussian state space models. Biometrika 84, 669-84.
11. FAHRMEIR, L. (1992). Posterior mode estimation by extended Kalman filtering for multivariate dynamic generalised linear models. J. Am. Statist. Assoc. 87, 501-9.
12. FRUHWIRTH-SCHNATTER, S. (1992). Approximate predictive integrals for dynamic generalized linear models. In Advances in GLIM and Statistical Modelling, Proceedings of the GLIM92 Conference and the 7th International Workshop on Statistical Modelling, Munich, 13-17 July 1992, Ed. L. Fahrmeir, B. Francis, R. Gilchrist and G. Tutz, pp. 101-6. New York: Springer-Verlag.
13. GILKS, W. K., RICHARDSON, S. & SPIEGELHALTER, D. J. (1996). Markov Chain Monte Carlo in Practice. London: Chapman and Hall.
14. GORDON, N. J., SALMOND, D. J. & SMITH, A. F. M. (1993). A novel approach to non-linear and non-Gaussian Bayesian state estimation. IEE Proc. F 140, 107-33.
15. GREEN, P. J. & HAN, X. L. (1992). Metropolis, Gaussian proposals and antithetic variables. In Stochastic Models, Statistical Methods and Algorithms in Image Analysis, 47, Ed. P. Barone, A. Frigessi and M. Piccioni, pp. 142-64. Berlin: Springer-Verlag.
16. HARVEY, A. C. (1989). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge: Cambridge University Press.
17. HARVEY, A. C. & FERNANDES, C. (1989). Time series models for count data or qualitative observations. J. Bus. Econ. Statist. 7, 407-17.
18. HARVEY, A. C., RUIZ, E. & SHEPHARD, N. (1994). Multivariate stochastic variance models. Rev. Econ. Studies 61, 247-64.
19. HULL, J. & WHITE, A. (1987). The pricing of options on assets with stochastic volatilities. J. Finance 42, 281-300.
20. JACQUIER, R., POLSON, N. G. & ROSSI, P. E. (1994). Bayesian analysis of stochastic volatility models (with Discussion). J. Bus. Econ. Statist. 12, 371-417.
21. KITAGAWA, G. (1987). Non-Gaussian state space modelling of non-stationary time series. J. Am. Statist. Assoc. 82, 503-14.
22. KOOPMAN, S. J. (1993). Disturbance smoother for state space models. Biometrika 80, 117-26.
23. LIU, J., WONG, W. H. & KONG, A. (1994). Covariance structure of the Gibbs sampler with applications to the comparison of estimators and augmentation schemes. Biometrika 81, 27-40.
24. MCCULLAGH, P. & NELDER, J. A. (1989). Generalized Linear Models, 2nd ed. London: Chapman and Hall.
25. MULLER, P. (1991). Numerical integration in general dynamic models. Contemp. Math. 115, 145-63.
26. PRIESTLEY, M. B. (1981). Spectral Analysis and Time Series. London: Academic Press.
27. RIPLEY, B. D. (1987). Stochastic Simulation. New York: Wiley.
28. SHEPHARD, N. (1994a). Local scale model: state space alternative to integrated GARCH processes. J. Economet. 60, 181-202.
29. SHEPHARD, N. (1994b). Partial non-Gaussian state space. Biometrika 81, 115-31.
30. SINGH, A. C. & ROBERTS, G. R. (1992). State space modelling cross-classified time series and counts. Int. Statist. Rev. 60, 321-35.
31. SMITH, J. Q. (1979). A generalization of the Bayesian steady forecasting model. J. R. Statist. Soc. B 41, 375-87.
32. SMITH, J. Q. (1981). The multiparameter steady model. J. R. Statist. Soc. B 43, 256-60.
33. SMITH, R. L. & MILLER, J. E. (1986). A non-Gaussian state space model and application to prediction records. J. R. Statist. Soc. B 48, 79-88.
34. TIERNEY, L. (1994). Markov Chains for exploring posterior distributions (with Discussion). Ann. Statist. 21, 1701-62.
35. WEST, M. (1993). Approximating posterior distributions by mixtures. J. R. Statist. Soc. B 55, 409-42.
36. WEST, M., HARRISON, P. J. & MIGON, H. S. (1985). Dynamic generalised models and Bayesian forecasting (with Discussion). J. Am. Statist. Assoc. 80, 73-97.