Autoregressive spectral analysis when observations are missing

Authors:
Piet M. T. Broersen;Stijn De Waele;Robert Bos
Affiliations:
Department of Multi Scale Physics, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands;Philips Research Laboratories, Eindhoven, The Netherlands;Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands
Venue:
Automatica (Journal of IFAC)
Year:
2004

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Abstract

A new missing data algorithm ARFIL gives good results in spectral estimation. The log likelihood of a multivariate Gaussian random variable can always be written as a sum of conditional log likelihoods. For a complete set of autoregressive AR(p) data the best predictor in the likelihood requires only p previous observations. If observations are missing, the best AR predictor in the likelihood will in general include all previous observations. Using only those observations that fall within a finite time interval will approximate this likelihood. The resulting non-linear estimation algorithm requires no user provided starting values. In various simulations, the spectral accuracy of robust maximum likelihood methods was much better than the accuracy of other spectral estimates for randomly missing data.