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

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 plus "noise".

If y(k) is the k-th value of the time series, the AR model of order N is given by:

where n(k) is the noise.
The AR coefficients can be estimated from the autocorrelation sequence by solving the Yule-Walker equations.
Once the AR model 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
 

References:
Marple SL Jr. (1987) Digital spectral analysis with applications. Prentice Hall, Englewood Cliffs, New Jersey
Fagard RH et al (1998)  Power spectral analysis of heart rate variability by autoregressive modelling and fast Fourier transform: a comparative study. Acta Cardiol.
Badilini F et al (1998) Heart rate variability in passive tilt test: comparative evaluation of autoregressive and FFT spectral analyses.Pacing Clin Electrophysiol
Christini DJ et al (1995)Influence of autoregressive model parameter uncertainty on spectral estimates of heart rate dynamics.  Ann Biomed Eng.
Pinna GD et al (1994) The accuracy of power-spectrum analysis of heart-rate variability from annotated RR lists generated by Holter systems. Physiol Meas.
Burr RL (1992) Autoregressive spectral models of heart rate variability. Practical issues. J Electrocardiol.
Fallen EL et al.(1988) Power spectrum of heart rate variability: a non-invasive test of integrated neurocardiac function. Clin Invest Med.
Baselli et al (1985) Autoregressive modeling and power spectral estimate of R-R interval time series in arrhythmic patients.  Comput Biomed Res
Haywood et al (1971) Clinical use of R-R interval prediction for ECG monitoring: time series analysis by autoregressive models. J Assoc Adv Med Instrum

(PC 10 Nov 2000)

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