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GLOSSARY OF TERMS USED IN TIME SERIES ANALYSIS OF CARDIOVASCULAR DATA

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Test suitable to detect nonlinear dynamics in short, noisy time series.

The basic concept of this procedure is to compare prediction results of linear and a nonlinear models fitted to the data. The relevance of nonlinear predictors is established when the best nonlinear model from the original data is significantly more predictive than both a) the best linear model form the time series, and b) the best linear and nonlinear models obtained from the surrogate data of the time series. The intriguing property of the method is that it functions reliably when up to 50% noise is added to the time series [see Barahona & Poon 1996]

Left: the linear prediction error is for all models less than the error for the nonlinear models. This indicates there is no type of nonlinear dynamics involved. Right: the two in the text mentionend conditions are fulfilled, suggesting that a relevant nonlinear dynamic process exists (the signal was derived from a Rössler-System).

Barahona-M, Poon-CS (1996) Detection of nonlinear dynamics in short, noisy time series Nature, Vol 381, 215-217
Poon CS, Merrill CK (1997) Decrease of cardiac chaos in congestive heart failure. Nature