autocorrelation

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autocorrelation

A measure of how closely a signal in a time series resembles a time-delayed image of itself—periodic signals are highly autocorrelated; random signals are not.
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The results of the above mentioned test as well as the results of the test with zero correlation coefficient between the bit autocorrelation function of the binary sequence analysed and standard bit autocorrelation functions
s1) having as reference goal the sidelobes reduction, the computation and analysis of the idealized shape assigned to the normalized envelope of the signal autocorrelation function [[rho].
The autocorrelation functions for return and residual series are very similar.
Sequences with a zero autocorrelation function can be used to generate orthogonal design matrices that achieve the optimal covariance matrix for the estimator of [?
The mathematical definition of a stationary process with long-memory or long-range dependence or persistence is given by its autocorrelation function [[rho].
Because the autocorrelation function is real and odd, if [tau] = 0, we can write:
Since x is a real sequence, the autocorrelation function is even, and so it is enough to prove the result for k > 0.
Therefore, I evaluated the autocorrelation function (ACF) and partial autocorrelation function (PACF) of the OLS regression residuals using SAS procedure PROC ARIMA (see SAS/ETS User's Guide, 1993).
The aperiodic autocorrelation function (ACF) of sequence S of length N is given as,
The above autocorrelation function of the signal, for moderately large numerical values of [tau], is described by an exponent C ([tau]) = exp (-[q.
In practice, a more adequate statistical measure of correlation content in any function is the autocorrelation function, C(r), which can range between -1 (very high negative correlation) and +1 (very high positive correlation), i.
These properties can be characterized by the autocorrelation function (ACF) and partial autocorrelation function (PACF).