Some applications of nonlinear and non-Gaussian state–space modelling by means of hidden Markov models

References

• Bartolucci , F. and De Luca , G. 2003 . Likelihood-based inference for asymmetric stochastic volatility models . Comput. Statist. Data Anal. , 42 ( 3 ) : 445 – 449 .
   Google Scholar
• Broto , C. and Ruiz , E. 2004 . Estimation methods for stochastic volatility models: a survey . J. Econom. Surveys , 18 ( 5 ) : 613 – 649 .
   Web of Science ®Google Scholar
• Cappé , O. , Moulines , E. and Rydén , T. 2005 . Inference in Hidden Markov Models , New York : Springer .
   Google Scholar
• Carlin , B. P. , Polson , N. G. and Stoffer , D. S. 1992 . A Monte Carlo Approach to Nonnormal and Nonlinear State-Space Modeling . J. Amer. Statist. Assoc. , 87 ( 418 ) : 439 – 500 .
   Google Scholar
• Chan , K. S. and Ledolter , J. 1995 . Monte Carlo EM Estimation for Time Series Models Involving Counts . J. Amer. Statist. Assoc. , 90 ( 429 ) : 242 – 252 .
   Web of Science ®Google Scholar
• Chib , S. , Nardari , F. and Shephard , N. 2002 . Markov chain Monte Carlo methods for stochastic volatility models . J. Econometrics , 108 ( 2 ) : 281 – 316 .
   Web of Science ®Google Scholar
• Davis , R. and Rodriguez-Yam , G. 2005 . Estimation for state–space models based on a likelihood approximation . Statist. Sinica , 15 ( 2 ) : 381 – 406 .
   Google Scholar
• Durbin , J. and Koopman , S. J. 1997 . Monte Carlo maximum likelihood estimation for non-Gaussian state space models . Biometrika , 84 ( 3 ) : 669 – 684 .
   Web of Science ®Google Scholar
• Durbin , J. and Koopman , S. J. 2001 . Time Series Analysis by State Space Methods , Oxford : Oxford University Press .
   Google Scholar
• Ephraim , Y. and Merhav , N. 2002 . Hidden Markov processes . IEEE Trans. Inform. Theory , 48 ( 6 ) : 1518 – 1569 .
   Web of Science ®Google Scholar
• Fokianos , K. , Rahbek , A. and Tjøstheim , D. 2009 . Poisson Autoregression . J. Amer. Statist. Assoc. , 104 ( 488 ) : 1430 – 1439 .
   Web of Science ®Google Scholar
• Fridman , M. and Harris , L. 1998 . A maximum likelihood approach for non-Gaussian stochastic volatility models . J. Business Econom. Statist. , 16 ( 3 ) : 284 – 291 .
   Web of Science ®Google Scholar
• Harvey , A. C. 1989 . Forecasting, Structural Time Series Models and the Kalman Filter , Cambridge : Cambridge University Press .
   Google Scholar
• Julier , S. J. and Uhlmann , J. K. 2004 . Unscented filtering and nonlinear estimation . Proc. IEEE , 92 ( 3 ) : 401 – 422 .
   Web of Science ®Google Scholar
• Kitagawa , G. 1987 . Non-Gaussian state–space modeling of nonstationary time series (with discussion) . J. Amer. Statist. Assoc. , 82 ( 400 ) : 1032 – 1063 .
   Web of Science ®Google Scholar
• Kitagawa , G. 1996 . Monte Carlo filter and smoother for non-Gaussian nonlinear state space models . J. Comput. Graph. Statist. , 5 ( 1 ) : 1 – 25 .
   Google Scholar
• Koopman , S. J. , Shephard , N. and Doornik , J. 1999 . Statistical algorithms for models in state space using SsfPack 2.2 . Econometrics J. , 2 ( 1 ) : 113 – 166 .
   Google Scholar
• Langrock , R. and Zucchini , W. 2011 . Hidden Markov models with arbitrary dwell-time distributions . Comput. Statist. Data Anal. , 55 ( 1 ) : 715 – 724 .
   Web of Science ®Google Scholar
• Le Strat , Y. and Carrat , F. 1999 . Monitoring epidemiologic surveillance data using hidden Markov models . Statist. Med. , 18 ( 24 ) : 3463 – 3478 .
   PubMed Web of Science ®Google Scholar
• Melino , A. and Turnbull , S. M. 1990 . Pricing foreign currency options with stochastic volatility . J. Econometrics , 45 ( 1–2 ) : 239 – 265 .
   Web of Science ®Google Scholar
• Rosenblatt , M. 1952 . Remarks on a multivariate transformation . Ann. Math. Statist. , 23 ( 3 ) : 470 – 472 .
   Google Scholar
• Schluter , C. and Trede , M. 2008 . Identifying multiple outliers in heavy-tailed distributions with an application to market crashes . J. Empirical Finance , 15 ( 4 ) : 700 – 713 .
   Web of Science ®Google Scholar
• Shephard , N. 1996 . “ Statistical aspects of ARCH and stochastic volatility ” . In Time Series Models: In econometrics, finance and other fields , Edited by: Cox , D. R. , Hinkley , D. V. and Barndorff-Nielsen , O. E. 1 – 67 . London : Chapman & Hall .
   Google Scholar
• Shumway , R. H. and Stoffer , D. S. 2006 . Time Series Analysis and Its Applications: With R Examples , 2 , Berlin : Springer .
   Google Scholar
• Srikanthan , R. and McMahon , T. A. 2001 . Stochastic generation of annual, monthly and daily climate data: A review . Hydrol. Earth System Sci. , 5 ( 4 ) : 653 – 670 .
   Google Scholar
• Welch , G. and Bishop , G. 1995 . “ An Introduction to the Kalman filter ” . UNC-CH Computer Science Technical Report 95–041
   Google Scholar
• Woolhiser , D. A. 1992 . “ Modeling daily precipitation – Progress and problems ” . In Statistics in the Environmental and Earth Sciences , Edited by: Walden , A. T. and Guttorp , P. 71 – 89 . New York : Edward Arnold, John Wiley .
   Google Scholar
• Zeger , S. L. 1988 . A regression model for time series of counts . Biometrika , 75 ( 4 ) : 621 – 629 .
   Web of Science ®Google Scholar
• Zucchini , W. and MacDonald , I. L. 2009 . Hidden Markov Models for Time Series: An Introduction Using R , London : Chapman & Hall .
   Google Scholar