# autocorrelation function

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## autocorrelation function

(aw-toh-kor-ĕ-lay -shŏn) A mathematical function that for a real function f(t) is given by
(u )f(u t )du

It describes, for example, the time or distance over which a signal is coherent. The cross-correlation function describes how two different signals compare as they are displaced relative to one another; for two real functions f(t) and g(t ), it is given by

(u )g(u t )du

## autocorrelation function

[¦ȯd·ō‚kär·ə′lā·shən ‚fuŋk·shən]
(mathematics)
For a specified function f (t), the average value of the product f (t) f (t- τ), where τ is a time-delay parameter; more precisely, the limit as T approaches infinity of 1/(2 T) times the integral from -T to T of F (t) f (t- τ) dt.
References in periodicals archive ?
Generalized Langevin equation with multiplicative noise: temporal behavior of the autocorrelation functions.
A second-order stationary process X is called exactly second-order self-similar (ESOSS) with Hurst parameter H=1-[beta]/2, 0<[beta]<1, if the autocorrelation function satisfies
The autocorrelation function of an ergodic process in the limited interval n=[0, N-1], k=[0, N-1] is calculated as a finite sum, (Marie, 2002) eq.
where [tau] is the decay time of the time autocorrelation function of the scattered electric field [g.
The autocorrelation function and partial autocorrelation function for equation 2 indicate that the residuals for equation 2 are white noise.
The magnitude of the sample autocorrelation function is shown in Figure 2; the data are significantly autocorrelated ([alpha] = .
However, further examination of the partial autocorrelation function finds that [r.
The growth rate and autocorrelation function of the adjusted monetary base, for our full sample and three subperiods, are shown in Figure 2.
We evaluated the autocorrelation function and partial autocorrelation function of the OLS regression residuals using SAS procedure PROC ARIMA (see SAS/ETS User's Guide, 1993).
ij] lie on a smooth surface whose spatial autocorrelation function is equal to j times that of h.
The positive correlation may, in part, result from a broad minimum of the autocorrelation function of the mean monthly Nino-3 index at lags from 16 to 28 months, with autocorrelation values of-0.
The power spectrum is the Fourier transform of the autocorrelation function of a time series.

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