Bootstrap approximation to prediction MSE for state-space models with estimated parameters

Journal of Time Series Analysis

Volumn 26, Issue 6, 2005, Pages 893-916

  Pfeffermann, Danny ^a   Tiller, Richard ^b  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b NONE

Author keywords

Hyper parameters; Kalman filter; MLE; Order of bias; REML

Indexed keywords

EID: 27644554896     PISSN: 01439782     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9892.2005.00448.x     Document Type: Article

References (20)

1. ANSLEY, C. F. and KOHN, R. (1986) Prediction mean squared error for state space models with estimated parameters. Biometrika 73, 467-73.
2. Box, G. E. P. and JENKINS, G. M. (1976) Time Series Analysis: Forecasting and Control (2nd edn). San Francisco, CA: Holden-Day.
3. DATTA, G.S., LAHIRI, P. and LU, K. L. (1999) Hierarchical Bayes estimation of unemployment rates for the states of the U.S. Journal of the American Statistical Association 94, 1074-82.
4. DE JONG, P. (1989) Smoothing and interpolation with the state-space model. Journal of the American Statistical Association 84, 1085-8.
5. DURBIN, J. and KOOPMAN, S. J. (2000) Time series analysis of non-Gaussian observations based on state-space models from both classical and Bayesian perspectives (with discussion). Journal of the Royal Statistical Society Series B 62, 3-56.
6. HALL, P. and MARTIN, M. A. (1988) On bootstrap resampling and iteration. Biometrika 75, 661-71.
7. HAMILTON, J. D. (1986) A standard error for the estimated state vector of a state space model. Journal of Econometrics 33, 387-97.
8. HARVEY, A. C. (1989) Forecasting Structural Time Series with the Kalman Filter. Cambridge: Cambridge University Press.
9. KOOPMAN, S. J., HARVEY, A. C., DOORNIK, J. A. and SHEPHARD, N. (1995) Stamp 5.0-Structural Time Series Analyser, Modeller and Predictor. London: Chapman & Hall.
10. PFEFFERMANN, D. (2002) Small area estimation - new developments and directions. International Statistical Review 70, 125-43.
11. PFEFFERMANN, D., FEDER, M. and SIGNORELLI, D. (1998) Estimation of autocorrelations of survey errors with application to trend estimation in small areas. Journal of Business and Economic Statistics 16, 339-48.
12. QUENNEVILLE, B. and SINGH, A. C. (2000) Bayesian prediction mean square error for state space models with estimated parameters. Journal of time series Analysis 21, 219-36.
13. SALLAS, W. H. and HARVILLE, D. A. (1981) Best linear recursive estimation for mixed linear models. Journal of the American Statistical Association 76, 860-9.
14. SHAO, J. and TU, D. (1995) The Jackknife and the Bootstrap. New York: Springer-verlag.
15. SINGH, A. C. STUKEL, D. M. and PFEFFERMANN, D. (1998) Bayesian versus frequentist measures of error in small area estimation. Journal of the Royal Statistical Society Series B 60, 377-96.
16. STOFFER, D.S. and WALL, K. D. (1991) Bootstrapping state-space models: Gaussian maximum likelihood estimation and the Kalman filter. Journal of the American Statistical Association 86, 1024-33.
17. STOFFER, D. S. and WALL, K. D. (2004) Resampling in state space models. In State Space and Unobserved Component Models, Theory and Application (eds A. Harvey, S. J. Koopman and N. Shephard). Cambridge: Cambridge University Press, pp. 171-202.
18. TILLER, R. B. (1992) Time series modeling of sample survey data from the U.S. Current population survey. Journal of Official Statistics 8, 149-66.
19. TSIMIKAS J. and LEDOLTER, J. (1994) REML and best linear unbiased prediction in state space models. Communication in Statistics, Theory and Methods 23, 2253-68.
20. WATANABE, N. (1985) Note on the Kalman filter with estimated parameters. Journal of Time Series Analysis 6, 269-78.