title: Tutorial on multivariate autoregressive modelling.
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.
authors.affiliation: Measurement and Information Technology, Tampere University of Technology, P.O. Box 692, FIN-33101, Tampere, Finland. heli.hytti@tut.fi
authors.forename: Heli
authors.initials: H
authors.lastname: Hytti
authors.forename: Reijo
authors.initials: R
authors.lastname: Takalo
authors.forename: Heimo
authors.initials: H
authors.lastname: Ihalainen
mesh_terms: D001698:Biomedical Engineering / Q000379:methods*; D001794:Blood Pressure; D002319:Cardiovascular System / Q000473:pathology*; D006801:Humans; D008955:Models, Cardiovascular; D015233:Models, Statistical; D008962:Models, Theoretical; D015999:Multivariate Analysis; D012044:Regression Analysis; D012119:Respiration; D012815:Signal Processing, Computer-Assisted; D013599:Systole