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GLOSSARY OF TERMS USED IN TIME SERIES ANALYSIS OF CARDIOVASCULAR DATA

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Mathematical modeling of a time series based on the assumption that each value of the series depends only on a weighted sum of the previous values of the same series (autoregressive component) and on a weighted sum of the present and previous values of a different time series (moving average component) with the addition of a "noise" factor.

If y(k) is the k-th value of the time series to model, u(k) a different time series and n(k) is noise, then ARMA model of order (N,M) is given by:

Once the ARMA model of a signal is estimated, the spectrum of the input signal can be computed as:

where is the variance of n(k) and T is the sampling interval (Marple, 1987). A comparison between AR and ARMA modelling of HR time series can be found in (Christini et al.,1995). ARMA analysis was used to parameterize the relations of respiration and arterial blood pressure to heart rate (Triedman et al., 1995) and to assess the baroreflex gain (Patton et al, 1996; O'Leary et al, 1999)

References:
Marple SL Jr.(1987) Digital spectral analysis with applications. Prentice Hall, Englewood Cliffs, New Jersey
Christini DJ et al (1995) Application of linear and nonlinear time series modeling to heart rate dynamics analysis.  IEEE Trans Biomed Eng.
Triedman JK et al (1995) Respiratory sinus arrhythmia: time domain characterization using autoregressive moving average analysis. Am J Physiol.
Patton DJ et al ,(1996)  Baroreflex gain: characterization using autoregressive moving average analysis. Am J Physiol.
 O'Leary DD et al (1999) Determination of baroreflex gain using auto-regressive moving-average analysis during spontaneous breathing. Clin Physiol. 1999 Sep;19(5):369-77.