GLOSSARY OF TERMS USED IN TIME SERIES ANALYSIS
OF CARDIOVASCULAR DATA
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RESCALED RANGE

Measure characterising the divergence of time series defined as the range of the sum of the deviations of data from the mean divided by the sample standard deviation

Both range R and standard deviation S measure the divergence of the time-series, but the first is a measure of dispersion based on a sum of the data, the second is a measure based on the squared data. For some processes (like white Gaussian noise, which has no persistence) the two measures of dispersion are similar and R/S is asymptotically constant with T, duration of the data sample. For other processes (like Brownian motion) R/S is proportional to a power of T:

R/S := TH
(the exponent H is called Hurst exponent). This exponential law reflects a long-term dependence, or persistence, in the process.

Bassingthwaighte JB, Raymond GM (1994) Evaluating rescaled range analysis for time series Ann Biomed Eng

(PC 22-12-1999)

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