# autocorrelation

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## autocorrelation

(ˌɔːtəʊˌkɒrɪˈleɪʃən)
n
(Statistics) the condition occurring when successive items in a series are correlated so that their covariance is not zero and they are not independent. Also called: serial correlation
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and Lambert-Lacroix, S., "Characterization of the Partial Autocorrelation Function of Non-Stationary Time Series," Journal of Multivariate Analysis 87:46-59, 2003.
Analysis was carried out using Wessa online: Wessa P., (2017), (Partial) Autocorrelation Function (v1.0.15) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL http://www.wessa.net/rwasp_autocorrelation.wasp.
Wherein: [tau] is the delay time of autocorrelation function; T is the value of time span.
We analyzed and discussed these data thoroughly and the plot of autocorrelation functions. However, by following the four steps in Box-Jenkins method, model identification, parameter estimation, diagnostic checking and forecasting, we conclude that Box-Jenkins model not suitable compare to single exponential and Holt's.
According to [9], the autocorrelation function is a constant times the inverse Fourier transform of the power spectral density function [P.sub.n]([omega]) of the air's refractive index n:
In microrheology experiments based on light scattering, the autocorrelation function of the intensity scattered by the tracers is measured.
Figure 1(a) shows the intensity autocorrelation function obtained for the bare microemulsion measurements.
The autocorrelation function of the BOC sequence can be expressed as [13]
(2) Model identification: the initial ARIMA (p, d, q) model gained from autocorrelation function (ACF) and partial autocorrelation function (PACF) of the processed time series could determine autoregression order (p) and order of moving average (q) preliminary.
The autocorrelation function of the output process X (t) is calculated as [15]

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