Time delay estimation with hidden Markov models

Mehdi Azzouzi, Ian T. Nabney

Research output: Chapter in Book/Published conference outputChapter


Most traditional methods for extracting the relationships between two time series are based on cross-correlation. In a non-linear non-stationary environment, these techniques are not sufficient. We show in this paper how to use hidden Markov models to identify the lag (or delay) between different variables for such data. Adopting an information-theoretic approach, we develop a procedure for training HMMs to maximise the mutual information (MMI) between delayed time series. The method is used to model the oil drilling process. We show that cross-correlation gives no information and that the MMI approach outperforms maximum likelihood.
Original languageEnglish
Title of host publicationNinth International Conference on Artificial Neural Networks, 1999 (ICANN)
Place of PublicationEdinburgh, UK
Number of pages6
ISBN (Print)0852967217
Publication statusPublished - 1999
EventNinth International conference on Artificial Neural Networks -
Duration: 1 Jan 19991 Jan 1999


ConferenceNinth International conference on Artificial Neural Networks

Bibliographical note

©1999 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.


  • time series
  • cross-correlation
  • non-stationary
  • Markov models
  • information-theoretic
  • mutual information


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