Heimo Ihalainen | PubMed Health

PubMed2006

Tutorial on multivariate autoregressive modelling.

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.

Biomedical Engineering↗

PubMed2006

Tutorial on univariate autoregressive spectral analysis.

In the present paper, the theoretical basis of autoregressive (AR) modelling in spectral analysis is explained in simple terms. Spectral analysis gives information about the frequency content and sources of variation in a time series. The AR method is an alternative to discrete Fourier transform, and the method of choice for high-resolution spectral estimation of a short time series. In biomedical engineering, AR modelling is used especially in the spectral analysis of heart rate variability and electroencephalogram tracings. In AR modelling, each value of a time series is regressed on its past values. The number of past values used is called the model order. An AR model or process may be used in either process synthesis or process analysis, each of which can be regarded as a filter. The AR analysis filter divides the time series into two additive components, the predictable time series and the prediction error sequence. When the prediction error sequence has been separated from the modelled time series, the AR model can be inverted, and the prediction error sequence can be regarded as an input and the measured time series as an output to the AR synthesis filter. When a time series passes through a filter, its amplitudes of frequencies are rescaled. The properties of the AR synthesis filter are used to determine the amplitude and frequency of the different components of a time series. Heart rate variability data are here used to illustrate the method of AR spectral analysis. Some basic definitions of discrete-time signals, necessary for understanding of the content of the paper, are also presented.

Heart Rate↗