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GLOSSARY OF
TERMS
USED
IN
TIME SERIES
ANALYSIS
OF CARDIOVASCULAR
DATA
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AUTOCORRELATION FUNTION
Measure of the dependence of time
series values at one time on the values at another time.
Given the time series x(n), n=1, 2, ...N, the autocorrelation
function at lag k is defined as:
The value of the autocorrelation function at lag 0 is the power
of x(n), or its variance if the mean value of x(n) is zero:
Moreover, 
is
the mean value for random processes.
The autocorrelation function may be used to detect deterministic components
masked in a random background because autocorrelation functions of deterministic
data (like sine wave) persist over all time displacements, while autocorrelation
functions of stocastic processes tend to zero for large time displacement
(for 0-mean time series).
See also Power Spectral Density.
References:
Bendat-JS, Persol-AG (1986) Random Data - Analysis
and Measurement Procedures, 2nd Edition, John Wiley & Sons, NY
(PC 24-09-1999)
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