Delay estimation for multivariate time series

Mehdi Azzouzi, Ian T. Nabney

Research output: Working paperTechnical report

Abstract

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

Fingerprint

Hidden Markov models
Time series
Maximum likelihood estimation
Drilling

Bibliographical note

Submitted to Pattern Analysis and Machine Intelligence

Keywords

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

Cite this

Azzouzi, M., & Nabney, I. T. (1998). Delay estimation for multivariate time series. Aston University, Birmingham, UK: Aston University.
Azzouzi, Mehdi ; Nabney, Ian T. / Delay estimation for multivariate time series. Aston University, Birmingham, UK : Aston University, 1998.
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Azzouzi, M & Nabney, IT 1998 'Delay estimation for multivariate time series' Aston University, Aston University, Birmingham, UK.

Delay estimation for multivariate time series. / Azzouzi, Mehdi; Nabney, Ian T.

Aston University, Birmingham, UK : Aston University, 1998.

Research output: Working paperTechnical report

TY - UNPB

T1 - Delay estimation for multivariate time series

AU - Azzouzi, Mehdi

AU - Nabney, Ian T.

N1 - Submitted to Pattern Analysis and Machine Intelligence

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

KW - lag detection

KW - hidden Markov models

KW - non-stationarity

KW - regime switching

KW - EM algorithm

KW - mutual information

M3 - Technical report

SN - NCRG/98/026

BT - Delay estimation for multivariate time series

PB - Aston University

CY - Aston University, Birmingham, UK

ER -

Azzouzi M, Nabney IT. Delay estimation for multivariate time series. Aston University, Birmingham, UK: Aston University. 1998.