Delay estimation for multivariate time series

Mehdi Azzouzi, Ian T. Nabney

Research output: Preprint or Working paperTechnical report


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 (HMMs) to identify the lag (or delay) between different variables for such data. We first present a method using maximum likelihood estimation and propose a simple algorithm which is capable of identifying associations between variables. We also adopt an information-theoretic approach and develop a novel procedure for training HMMs to maximise the mutual information between delayed time series. Both methods are successfully applied to real data. We model the oil drilling process with HMMs and estimate a crucial parameter, namely the lag for return.
Original languageEnglish
Place of PublicationAston University, Birmingham, UK
PublisherAston University
Number of pages18
ISBN (Print)NCRG/98/026
Publication statusPublished - 1998

Bibliographical note

Submitted to Pattern Analysis and Machine Intelligence


  • lag detection
  • hidden Markov models
  • non-stationarity
  • regime switching
  • EM algorithm
  • mutual information


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