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Tutorial on Multivariate Autoregressive Modelling

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Abstract

In the present paper, the theoretical background of multivariate autoregressive modelling (MAR) is explained. The motivation for MAR modelling is the need to study the linear relationships between signals. In biomedical engineering, MAR modelling is used especially in the analysis of cardiovascular dynamics and electroencephalographic signals, because it allows determination of physiologically relevant connections between the measured signals. In a MAR model, the value of each variable at each time instance is predicted from the values of the same series and those of all other time series. The number of past values used is called the model order. Because of the inter-signal connections, a MAR model can describe causality, delays, closed-loop effects and simultaneous phenomena. To provide a better insight into the subject matter, MAR modelling is here illustrated with a model between systolic blood pressure, RR interval and instantaneous lung volume.

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Authors and Affiliations

  1. Measurement and Information Technology, Tampere University of Technology, P.O. Box 692, FIN-33101, Tampere, Finland

    Heli Hytti MSc (Tech) & Heimo Ihalainen MSc(Tech)

  2. Division of Nuclear Medicine, Laboratory, Oulu University Hospital, P.O. Box 500, FIN-90020 OYS, Oulu, Finland

    Reijo Takalo MD, PhD

Authors
  1. Heli Hytti MSc (Tech)
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  2. Reijo Takalo MD, PhD
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  3. Heimo Ihalainen MSc(Tech)
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Correspondence to Heli Hytti MSc (Tech).

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Hytti, H., Takalo, R. & Ihalainen, H. Tutorial on Multivariate Autoregressive Modelling. J Clin Monit Comput 20, 101–108 (2006). https://doi.org/10.1007/s10877-006-9013-4

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  • DOI: https://doi.org/10.1007/s10877-006-9013-4

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