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Current Development in Theory and Applications of Wavelets

Current Development in Theory and Applications of Wavelets
Volume 3, Issue 1, Pages 1 - 30 (April 2009)

WAVELET ESTIMATION OF STATE SPACE MODELS Airlane P. Alencar (Brazil), Pedro A. Morettin (Brazil), Clélia M. C. Toloi (Brazil) and Eliana Zandonade (Brazil) Received January 21, 2009 References:
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Dahlhaus, Maximum likelihood estimation and model selection for locally stationary processes, J. Nonparametric Statistics 6 (1996), 171-191. [9] R. Dahlhaus, Fitting time series models to nonstationary processes, Ann. Stat. 25 (1997a), 1-37. [10] R. Dahlhaus, The Analysis of Nonstationary Time Series and Curve Estimation with Locally Stationary Models, Institute of Statistical Sciences, Academia Sinica, 1997b. [11] R. Dahlhaus, M. H. Neumann and R. von Sachs, Nonlinear wavelet estimation of the time-varying autoregressive processes, Bernoulli 5 (1999), 873-906. [12] I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, 1992. [13] A. P. Dempster, N. M. Laird and D. B. Rubin, Maximum likelihood from incomplete data via the EM algorithm, J. Royal Stat. Soc. Ser. B 39 (1997), 1-38. [14] F. X. Diebold, J. H. Lee and G. C. Weinbach, Regime switching with time varying transition probabilities, Nonstationary Time Series Analysis and Cointegration, C. Hargreaves, ed., Oxford University Press, Oxford, 1994, pp. 283-302. [15] D. L. Donoho, X. Huo, M. Duncan and O. Levi-Tsabari, About Wave-Lab, Stanford University, 2000, http://www.stat.stanford.edu/~ wavelab. [16] J. Durbin and S. J. Koopman, Monte Carlo maximum likelihood estimation for non-Gaussian state space models, Technical Report, London School of Economics and Political Science, London, UK, 1996. [17] J. Durbin and S. J. Koopman, Time Series Analysis by State Space Methods, Oxford University Press, Oxford, 2001. [18] L. Fahrmeir, State space modelling and conditional mode estimation for categorical time series, New Directions in Time Series Analysis, Part I, Springer, New York, 1992, pp. 87-109. [19] A. J. Filardo, Business cycle phases and their transitional dynamics, J. Bus. Econom. Statist. 78 (1994), 111-125. [20] R. Fletcher, Practical Methods of Optimization, Wiley, Padstow, 1987. [21] S. M. Goldfeld and R. E. Quandt, A Markov model for switching regression, J. Econometrics 1 (1973), 3-16. [22] J. D. Hamilton, A new approach to the economic analysis of nonstationary time series and the business cycle, Econometrica 57 (1989), 357-384. [23] J. D. Hamilton, Analysis of time series subject to changes in regime, J. Econometrics 45 (1990), 39-70. [24] J. D. Hamilton, Time Series Analysis, Princeton University Press, New Jersey, 1994. [25] P. J. Harrison and C. F. Stevens, Bayesian forecasting, J. Royal Stat. Soc. Ser. B 38 (1976), 205-247. [26] A. C. Harvey, Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge University Press, Cambridge, 1989. [27] C. J. Kim, Dynamic linear models with Markov switching, J. Econometrics 60 (1994), 1-22. [28] C. J. Kim and C. R. Nelson, State Space Models with Regime Switching, The MIT Press, Cambridge, 1999. [29] G. Kitagawa and W. Gersch, Smoothness priors analysis of time series, Lecture Notes in Statistics, Vol. 116, Springer, 1996. [30] K. D. Koch, Parameter Estimation and Hypothesis Testing in Linear Models, Springer-Verlag, Berlin, 1999. [31] R. J. Meinhold and N. D. Singpurwalla, Understanding the Kalman filter, The American Statistician 37 (1983), 123-127. [32] R. J. Meinhold and N. D. Singpurwalla, A Kalman-filter smoothing approach for extrapolation in certain dose-response, damage-assessment, and accelerated-life testing studies, The American Statistician 41 (1987), 101-106. [33] R. J. Meinhold and N. D. Singpurwalla, Robustification of Kalman filter models, J. Amer. Statist. Assoc. 84 (1989), 479-486. [34] Y. Meyer, Wavelets: Algorithms and Applications, SIAM, Philadelphia, 1993. [35] P. A. Morettin, Wavelets in statistics, São Paulo J. Math. Sci. 3 (1997), 211-272. [36] G. Nason and B. Silverman, The discrete wavelet transform in S, J. Comput. Graph. Statist. 3 (1994), 163-191. [37] D. B. Percival and A. T. Walden, Wavelet Methods for Time Series, Cambridge University Press, Cambridge, 2000. [38] R. E. Quandt, A new approach to estimating switching regressions, J. Amer. Statist. Assoc. 67 (1972), 306-310. [39] T. Sáfadi and P. A. Morettin, Bayesian analysis of threshold autoregressive moving average models, Sankhya Ser. B 62 (2000), 353-371. [40] R. H. Shumway, D. E. Olsen and L. J. Levy, Estimation and tests of hypotheses for the initial mean and covariance in the Kalman filter model, Comm. Statist. Theory Methods 10 (1981), 1625-1641. [41] R. H. Shumway and D. S. Stoffer, An approach to time series smoothing and forecasting using the EM algorithm, J. Time Ser. Anal. 3 (1982), 253-264. [42] R. H. Shumway and D. S. Stoffer, Dynamic linear models with switching, J. Amer. Statist. Assoc. 86 (1991), 763-769. [43] R. H. Shumway and D. S. Stoffer, Time Series Analysis and its Applications: With R Examples, Springer, New York, 2006. [44] D. S. Stoffer and K. D. Wall, Bootstrapping state-space models: Gaussian maximum likelihood estimation and the Kalman filter, J. Amer. Statist. 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Keywords and phrases: EM algorithm, Kalman filter, Markov chain, state space models, switching models, wavelets.

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