Autocorrelation, sometimes known as serial correlation in the discrete time case, measures the correlation of a signal with a delayed copy of itself....

In optics, various autocorrelation functions can be experimentally realized. The field autocorrelation may be used to calculate the spectrum of a source...

Phylogenetic autocorrelation also known as Galton's problem, after Sir Francis Galton who described it, is the problem of drawing inferences from cross-cultural...

In time series analysis, the partial autocorrelation function (PACF) gives the partial correlation of a stationary time series with its own lagged values...

In combinatorics, a branch of mathematics, the autocorrelation of a word is the set of periods of this word. More precisely, it is a sequence of values...

statistics. For example, in time series analysis, a plot of the sample autocorrelations r h {\displaystyle r_{h}\,} versus h {\displaystyle h\,} (the time...

Spatial dependency leads to the spatial autocorrelation problem in statistics since, like temporal autocorrelation, this violates standard statistical techniques...

differencing it if necessary), and using plots of the autocorrelation (ACF) and partial autocorrelation (PACF) functions of the dependent time series to decide...

The autocorrelation technique is a method for estimating the dominating frequency in a complex signal, as well as its variance. Specifically, it calculates...

Wiener–Khinchin–Einstein theorem or the Khinchin–Kolmogorov theorem, states that the autocorrelation function of a wide-sense-stationary random process has a spectral decomposition...

Moran's I is a measure of spatial autocorrelation developed by Patrick Alfred Pierce Moran. Spatial autocorrelation is characterized by a correlation...

Barker sequence is a finite sequence of digital values with the ideal autocorrelation property. It is used as a synchronising pattern between the sender...

variable as X, the above expressions are called the autocovariance and autocorrelation: autocovariance σ X X ( m ) = E [ ( X n − μ X ) ( X n + m − μ X ) ]...

Zero AutoCorrelation waveform (CAZAC) is a periodic complex-valued signal with modulus one and out-of-phase periodic (cyclic) autocorrelations equal...

at pairs of time points. Autocovariance is closely related to the autocorrelation of the process in question. With the usual notation E {\displaystyle...

number of later variants. The estimator is used to try to overcome autocorrelation (also called serial correlation), and heteroskedasticity in the error...

sequences with the useful property that their out-of-phase aperiodic autocorrelation coefficients sum to zero. Binary complementary sequences were first...

However, the daily data in the example may have too much noise, temporal autocorrelation, or be inconsistent with other datasets. With only daily data, conducting...

temporal fluctuations are usually analyzed using the intensity or photon autocorrelation function (also known as photon correlation spectroscopy – PCS or quasi-elastic...

of a true autocorrelation—has not been found. At least one model shows that a temporal delay is unnecessary to produce an autocorrelation model of pitch...

_{k=1}^{\infty }\rho _{k}} , is often called the integrated autocorrelation. When the chain has no autocorrelation ( ρ k = 0 {\displaystyle \rho _{k}=0} for all k...

points, then this is often referred to as an autocorrelation function, which is made up of autocorrelations. Correlation functions of different random variables...

analysis and market forecasting. There are two algorithms based on autocorrelation functions that can identify the dominant noise type in a data set provided...

Decorrelation is a general term for any process that is used to reduce autocorrelation within a signal, or cross-correlation within a set of signals, while...

Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model...

ones in the truth table. Bent: its derivatives are all balanced (the autocorrelation spectrum is zero) Correlation immune to mth order: if the output is...

as a measure of long-term memory of time series. It relates to the autocorrelations of the time series, and the rate at which these decrease as the lag...

P. Box) is a type of statistical test of whether any of a group of autocorrelations of a time series are different from zero. Instead of testing randomness...

"correlation function" refers to the two-point autocorrelation function. The two-point autocorrelation function is a function of one variable (distance);...

generating data for y t {\displaystyle y_{t}} might have a higher order of autocorrelation than is admitted in the test equation—making y t − 1 {\displaystyle...