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.

A system identification approach to baroreflex sensitivity estimation

“…Baselli et al [13] use a closed-loop model to represent the relationship between RR, SAP and respiration (RESP ), while in another approach which respects the closed-loop nature of the baroreflex, bivariate autoregressive modelling has been employed to calculate the transfer functions between the signals on the feed-forward and feed-back side of the loop simultaneously [14]. A number of researchers [15,16,17] take this approach to evaluate model components in the time domain and subsequently calculate the frequency response of these components.…”

Body sensor networks based sensor fusion for cardiovascular biosignal predictions

“…Various techniques are involved in sensor fusion, including autoregressive (AR) modeling [1], multivariate autoregressive (MAR) modeling [2][3], least square method, Bayesian networks, fuzzy logic [12], and artificial neural networks, etc. Compared with a univariate AR model, which is able to predict the current value of a time series from the previous values of the same time series [1], a multivariate AR model contains more information.…”

Separation of Dependent Autoregressive Sources Using Joint Matrix Diagonalization

“…Note that the AR structure is widely used for different kind of signals such as harmonics, speech, cardiovascular dynamics and electroencephalographic signals [5]. Separation of AR sources has been the focus of many research papers for the case of independent sources, e.g.…”