GLOSSARY OF TERMS USED IN TIME SERIES ANALYSIS
OF CARDIOVASCULAR DATA
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 BIVARIATE AUTOREGRESSIVE MODELING

Modeling of two time-series based on the assumption that each value of the two series depends on a weighted sum of the previous values of the same series, plus a second weighted sum of the present and previous values of the other series, plus “noise”.

This type of parametric modeling has been used to describe the coupling between tachogram and systogram. If RR(n) and SBP(n) are the n-th values of the RR-interval and systolic blood pressure series, the bivariate autoregressive model is given by:

where wRR(n) and wSBP(n) are noises.
More generally, multivariate AR models can be used to describe the mutual interactions of more than two signals. For instance, the following trivariate AR system has been proposed to describe the interaction between heart interval, systolic blood pressure and respiration:

where RESP(n) is the respiractory activity at sample n.

Multivariate AR models can be expressed in the following matrix form:

where for the trivariate model above we have:

References:
Baselli G et al (1997) Spectral decomposition in multichannel recordings based on multivariate parametric identification. IEEE Trans Biomed Eng
Barbieri R et al (1997) Model dependency of multivariate autoregressive spectral analysis.  IEEE Eng Med Biol Mag.
Nollo G et al (2001) Causal linear parametric model for baroreflex gain assessment in patients with recent myocardial infarction. Am J Physiol 

(PC 10 Apr 2001)

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