Some Applications of the EM Algorithm to Analyzing Incomplete Time Series Data

Conference paper
Part of the Lecture Notes in Statistics book series (LNS, volume 25)


One may encounter incompletely specified time series data in several distinct forms: (1) observations in time or space may be irregularly observed or (2) the underlying time series model may be incompletely observed, as in the case where one observes only the sum of a signal and a noise process. Maximum likelihood estimators for parameters in these missing data problems can be developed in a simple, heuristically appealing form by utilizing the EM (expectation-maximization) algorithm proposed by Dempster, et al. (1977) and others. Furthermore, the conditional expectations computed as a by-product of applying the algorithm are the empirical Bayes (in the sense of Efron and Morris (1973), (1975)) estimators for the unobserved components. The EM algorithm is reviewed here within the time series context and applied to (i) the parameter estimation and smoothing problem for missing data state-space models and (ii) linear estimation (deconvolution) in a frequency domain regression model.


Discrete Fourier Transform Maximum Likelihood Estimator Conditional Expectation Noise Process Noise Spectrum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  1. 1.Division of StatisticsUniversity of CaliforniaDavisUSA

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