Correlation of a signal with a time-shifted copy of itself, as a function of shift
Part of a series on Statistics
Correlation and covariance
For random vectors
Autocorrelation matrix
Cross-correlation matrix
Auto-covariance matrix
Cross-covariance matrix
For stochastic processes
Autocorrelation function
Cross-correlation function
Autocovariance function
Cross-covariance function
For deterministic signals
Autocorrelation function
Cross-correlation function
Autocovariance function
Cross-covariance function
v
t
e
Above: A plot of a series of 100 random numbers concealing a sine function. Below: The sine function revealed in a correlogram produced by autocorrelation.Visual comparison of convolution, cross-correlation, and autocorrelation. For the operations involving function f, and assuming the height of f is 1.0, the value of the result at 5 different points is indicated by the shaded area below each point. Also, the symmetry of f is the reason and are identical in this example.
Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies. It is often used in signal processing for analyzing functions or series of values, such as time domain signals.
Different fields of study define autocorrelation differently, and not all of these definitions are equivalent. In some fields, the term is used interchangeably with autocovariance.
Unit root processes, trend-stationary processes, autoregressive processes, and moving average processes are specific forms of processes with autocorrelation.
Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function...
In time series analysis, the partial autocorrelation function (PACF) gives the partial correlation of a stationary time series with its own lagged values...
In optics, various autocorrelation functions can be experimentally realized. The field autocorrelation may be used to calculate the spectrum of a source...
statistics. For example, in time series analysis, a plot of the sample autocorrelations r h {\displaystyle r_{h}\,} versus h {\displaystyle h\,} (the time...
Phylogenetic autocorrelation also known as Galton's problem, after Sir Francis Galton who described it, is the problem of drawing inferences from cross-cultural...
temporal fluctuations are usually analyzed using the intensity or photon autocorrelation function (also known as photon correlation spectroscopy – PCS or quasi-elastic...
Barker sequence, is a finite sequence of digital values with the ideal autocorrelation property. It is used as a synchronising pattern between the sender...
Spatial dependency leads to the spatial autocorrelation problem in statistics since, like temporal autocorrelation, this violates standard statistical techniques...
The autocorrelation technique is a method for estimating the dominating frequency in a complex signal, as well as its variance. Specifically, it calculates...
sequences with the useful property that their out-of-phase aperiodic autocorrelation coefficients sum to zero. Binary complementary sequences were first...
chemical reactions, aggregation, etc.) are analyzed using the temporal autocorrelation. Because the measured property is essentially related to the magnitude...
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...
{\displaystyle \operatorname {K} _{\mathbf {X} \mathbf {X} }} is related to the autocorrelation matrix R X X {\displaystyle \operatorname {R} _{\mathbf {X} \mathbf...
chance, the spatial autocorrelation is said to be positive. When a pair of values are less similar, the spatial autocorrelation is said to be negative...
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 ) ]...
The autocorrelation function of an AR(p) process is a sum of decaying exponentials. Each real root contributes a component to the autocorrelation function...
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...
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...
Global Information
