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Correlation of a signal with a time-shifted copy of itself, as a function of shift
Autocorrelation, sometimes known as serial correlation in the discrete time case, measures the correlation of a signal with a delayed copy of itself.
Autocorrelation
Autocorrelation functions realized in optics
In optics, various autocorrelation functions can be experimentally realized. The field autocorrelation may be used to calculate the spectrum of a source
Optical_autocorrelation
Partial correlation of a time series with its lagged values
In time series analysis, the partial autocorrelation function (PACF) gives the partial correlation of a stationary time series with its own lagged values
Partial autocorrelation function
Partial_autocorrelation_function
Measure of spatial autocorrelation
Moran's I is a measure of spatial autocorrelation developed by Patrick Alfred Pierce Moran. Spatial autocorrelation is characterized by a correlation
Moran's_I
Method to find best fit of a time-series model
differencing it if necessary), and using plots of the autocorrelation (ACF) and partial autocorrelation (PACF) functions of the dependent time series to decide
Box–Jenkins_method
zero-autocorrelation waveform (CAZAC) is a periodic complex-valued signal with modulus one and out-of-phase periodic (cyclic) autocorrelations equal
Constant-amplitude zero-autocorrelation waveform
Constant-amplitude_zero-autocorrelation_waveform
Chart of correlation statistics
statistics. For example, in time series analysis, a plot of the sample autocorrelations r h {\displaystyle r_{h}} versus h {\displaystyle h\,} (the time lags)
Correlogram
Problem of drawing inferences from cross-cultural data
Phylogenetic autocorrelation, also known as Galton's problem after Sir Francis Galton who described it, is the problem of drawing inferences from cross-cultural
Phylogenetic_autocorrelation
Statistical tool
number of later variants. The estimator is used to try to overcome autocorrelation (also called serial correlation), and heteroskedasticity in the error
Newey–West_estimator
Theorem relating stationary processes' autocorrelations and power spectra
random process is equal to the Fourier transform of that process's autocorrelation function. Norbert Wiener proved this theorem for the case of a deterministic
Wiener–Khinchin_theorem
Signal with equal energy per octave
noise constrained to continuous frequencies from kmin to kmax, the autocorrelation coefficient is r ( d ) = Ci ( 2 π k max d N ) − Ci ( 2 π k min d N
Pink_noise
Pairs of sequences
sequences with the useful property that their out-of-phase aperiodic autocorrelation coefficients sum to zero. Binary complementary sequences were first
Complementary_sequences
Sequence of digital values used for synchronisation
Barker sequence is a finite sequence of digital values with the ideal autocorrelation property. It is used as a synchronising pattern between the sender
Barker_code
Procedure to estimate standard deviation from a sample
the autocorrelation function (ACF) of the data. (Note that the expression in the brackets is simply one minus the average expected autocorrelation for
Unbiased estimation of standard deviation
Unbiased_estimation_of_standard_deviation
Sequence of data points over time
and smoothing for more techniques. Other related techniques include: Autocorrelation analysis to examine serial dependence Spectral analysis to examine
Time_series
Techniques to study geometric data
Spatial dependency leads to the spatial autocorrelation problem in statistics since, like temporal autocorrelation, this violates standard statistical techniques
Spatial_analysis
In combinatorics, the autocorrelation of a word is the set of periods of this word
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
Autocorrelation_(words)
Type of matrix in probability theory and statistics
vectors Autocorrelation matrix Cross-correlation matrix Auto-covariance matrix Cross-covariance matrix For stochastic processes Autocorrelation function
Cross-covariance_matrix
Source of statistical bias
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
Modifiable temporal unit problem
Modifiable_temporal_unit_problem
Concepts in probability and statistics
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 ) ]
Covariance_and_correlation
The autocorrelation technique is a method for estimating the dominating frequency in a complex signal, as well as its variance. Specifically, it calculates
Autocorrelation_technique
Statistical property
bias coefficient ρ is the widely used Prais–Winsten estimate of the autocorrelation-coefficient (a quantity between −1 and +1) for all sample point pairs
Standard_error
Calculation of complex statistical distributions
_{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
Markov_chain_Monte_Carlo
Power spectrum of a noise signal
analysis and market forecasting. There are two algorithms based on autocorrelation functions that can identify the dominant noise type in a data set provided
Colors_of_noise
Statistical model used in time series analysis
determined using the sample autocorrelation function (ACF), partial autocorrelation function (PACF), and/or extended autocorrelation function (EACF) method
Autoregressive integrated moving average
Autoregressive_integrated_moving_average
Spatial autocorrelation statistic
are used in spatial analysis to measure the local and global spatial autocorrelation. Developed by statisticians Arthur Getis and J. Keith Ord they are
Getis–Ord_statistics
Technique for determining size distribution of particles
temporal fluctuations are usually analyzed using the intensity or photon autocorrelation function (also known as photon correlation spectroscopy – PCS or quasi-elastic
Dynamic_light_scattering
Concept in probability and statistics
at pairs of time points. Autocovariance is closely related to the autocorrelation of the process in question. With the usual notation E {\displaystyle
Autocovariance
Representation of a type of random process
The autocorrelation function of an AR(p) process is a sum of decaying exponentials. Each real root contributes a component to the autocorrelation function
Autoregressive_model
Perceptual property in music ordering sounds from low to high
levels is still debated, but the processing seems to be based on an autocorrelation of action potentials in the auditory nerve. However, it has long been
Pitch_(music)
interferometric autocorrelator is an electronic tool used to examine the autocorrelation of, among other things, optical beam intensity and spectral components
Autocorrelator
Small elements of a computer graphic
with each pixel associated with a vector of 9 texture attributes. The autocorrelation function of an image can be used to detect repetitive patterns of textures
Image_texture
Measure of spacial autocorrelation
Geary's C is a measure of spatial autocorrelation developed by Roy C. Geary. that attempts to determine if observations of the same variable are spatially
Geary's_C
Covariance and correlation
cross-correlation is similar in nature to the convolution of two functions. In an autocorrelation, which is the cross-correlation of a signal with itself, there will
Cross-correlation
Study of the distribution or space occupied by species
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
Spatial_ecology
Measure of covariance of components of a random vector
{\displaystyle \operatorname {K} _{\mathbf {X} \mathbf {X} }} is related to the autocorrelation matrix R X X {\displaystyle \operatorname {R} _{\mathbf {X} \mathbf
Covariance_matrix
Type of deterministic method for multivariate interpolation
method can also be used to create spatial weights matrices in spatial autocorrelation analyses (e.g. Moran's I). The name given to this type of method was
Inverse_distance_weighting
Phenomenon in economics and accounting
positive autocorrelations for the first three lags that decline in magnitude: First-order autocorrelation: approximately 0.34 Second-order autocorrelation: approximately
Post–earnings-announcement drift
Post–earnings-announcement_drift
Statistical model used in time series analysis
be found by plotting the partial autocorrelation functions. Similarly, q can be estimated by using the autocorrelation functions. Both p and q can be determined
Autoregressive moving-average model
Autoregressive_moving-average_model
Open conjecture that no real circulant Hadamard matrix has order greater than 4
exists. The problem has equivalent formulations in terms of periodic autocorrelation, discrete Fourier transforms, Littlewood polynomials, perfect binary
Ryser's conjecture on circulant Hadamard matrices
Ryser's_conjecture_on_circulant_Hadamard_matrices
Function returning one of only two values
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
Boolean_function
Audio processor that alters pitch
Macintosh computer. Hildebrand's method for detecting pitch involved autocorrelation and proved superior to attempts based on feature extraction, which
AutoTune
Process of reducing correlation within one or more signals
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
Decorrelation
Potential for two waves to interfere
defined as the Fourier transforms of the cross-correlation and the autocorrelation signals, respectively. For instance, if the signals are functions of
Coherence_(physics)
Class of stochastic process
identifying non-stationary time series is the ACF (Autocorrelation Function) plot, which plots the autocorrelation against the lag. Sometimes, patterns related
Stationary_process
Study of spatial information
other). Spatial autocorrelation involves the correlation of a variable with itself across different spatial locations. Temporal autocorrelation involves the
Technical_geography
Measures process correlation distance
{\displaystyle \rho (\tau )} and ρ ( r ) {\displaystyle \rho (r)} are the autocorrelation with respect to time and space respectively. In isotropic homogeneous
Integral_length_scale
Test statistic
Durbin–Watson statistic is a test statistic used to detect the presence of autocorrelation at lag 1 in the residuals (prediction errors) from a regression analysis
Durbin–Watson_statistic
Algorithm used for frequency estimation and radio direction finding
the p × p {\displaystyle p\times p} autocorrelation matrix of s {\displaystyle \mathbf {s} } . The autocorrelation matrix R x {\displaystyle \mathbf {R}
MUSIC_(algorithm)
Relative importance of certain frequencies in a composite signal
function S ¯ x x ( f ) {\displaystyle {\bar {S}}_{xx}(f)} and the autocorrelation of x ( t ) {\displaystyle x(t)} form a Fourier transform pair, a result
Spectral_density
Polynomial whose coefficients are all 1 or −1
{\displaystyle L^{q}} norms, Mahler measure, zero distribution, and autocorrelation remain active. A polynomial P ( z ) = ∑ j = 0 n a j z j {\displaystyle
Littlewood_polynomial
Method of frequency estimation
M} autocorrelation matrix are either known or estimated. Hence, given the ( p + 1 ) × ( p + 1 ) {\displaystyle (p+1)\times (p+1)} autocorrelation matrix
Pisarenko harmonic decomposition
Pisarenko_harmonic_decomposition
appreciable autocorrelation or cross-correlation in stochastic processes. The correlation coefficient ρ, expressed as an autocorrelation function or cross-correlation
Life-time_of_correlation
Acoustic phenomenon
of a true autocorrelation) have not been found. At least one model shows a temporal delay to be unnecessary to produce an autocorrelation model of pitch
Missing_fundamental
Function describing the distribution of galaxies in the universe
"correlation function" refers to the two-point autocorrelation function. The two-point autocorrelation function is a function of one variable (distance);
Correlation function (astronomy)
Correlation_function_(astronomy)
Mathematical operation that predicts future values of a discrete-time signal
a_{i}} is the root mean square criterion which is also called the autocorrelation criterion. In this method we minimize the expected value of the squared
Linear_prediction
Time series model
they combine both autoregressive and moving average components. The autocorrelation function (ACF) of an MA(q) process is zero at lag q + 1 and greater
Moving-average_model
Statistics of spatial association
analysis used to assess the degree of association, in particular the autocorrelation, of categorical variables distributed over a spatial map. They were
Join_count_statistic
Decision rules for interpreting control-chart data
the centerline with no points falling in zone C. Systematic Negative autocorrelation—a long series of observations that alternate high-low-high-low (No
Western_Electric_rules
Statistical relationship
correlation coefficient to multiple regression. Mathematics portal Autocorrelation Canonical correlation Coefficient of determination Cointegration Concordance
Correlation
Spectral density estimation method
corresponds to the most random or the most unpredictable time series whose autocorrelation function agrees with the known values. This assumption, which corresponds
Maximum entropy spectral estimation
Maximum_entropy_spectral_estimation
Correlation as a function of distance
points, then this is often referred to as an autocorrelation function, which is made up of autocorrelations. Correlation functions of different random variables
Correlation_function
Type of chart
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model
Bar_chart
Spatial correlation measure
data, in particular they are vulnerable to inflation due to spatial autocorrelation. Lee's L is available in numerous spatial analysis software libraries
Lee's_L
Free geovisualization and analysis software
package that conducts spatial data analysis, geovisualization, spatial autocorrelation and spatial modeling. It runs on different versions of Windows, Mac
GeoDa
Wireless positioning technology
increase the effective SNR and simultaneously exhibit a highly peaked autocorrelation function, in order to enhance synchronization accuracy. The second
UWB_ranging
Statistical test
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
Phillips–Perron_test
Statistical test
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
Ljung–Box_test
Concept in digital signal processing
}-\operatorname {E} [\mathbf {Z} ]\operatorname {E} [\mathbf {W} ]^{\rm {H}}} Autocorrelation Correlation does not imply causation Covariance function Pearson product-moment
Cross-correlation_matrix
Mathematical map
unit interval. The autocorrelation function for a sufficiently long sequence { x n {\displaystyle x_{n}} } will show zero autocorrelation at all non-zero
Tent_map
Range to estimate an unknown parameter
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model
Confidence_interval
Statistical model
Autocorrelation of a random lacunary Fourier series
Gaussian_process
Type of statistical analysis
chemical reactions, aggregation, etc.) are analyzed using the temporal autocorrelation. Because the measured property is essentially related to the magnitude
Fluorescence correlation spectroscopy
Fluorescence_correlation_spectroscopy
Signal processing technique
these components. These methods are based on eigendecomposition of the autocorrelation matrix into a signal subspace and a noise subspace. After these subspaces
Spectral_density_estimation
of the speckle pattern will be used to compute the contrast value. Autocorrelation functions of electric field are used to measure the relationship between
Laser speckle contrast imaging
Laser_speckle_contrast_imaging
Statistical interpretation with many tests
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model
Multiple_comparisons_problem
Method of statistical sampling
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model
Stratified_randomization
Statistical hypothesis test
portmanteau test in time-series analysis, testing for the presence of autocorrelation Likelihood-ratio tests in general statistical modelling, for testing
Chi-squared_test
Method of measuring spectral phase of ultrashort laser pulses
method called autocorrelation, which only gave a rough estimate for the pulse length. FROG is simply a spectrally resolved autocorrelation, which allows
Frequency-resolved optical gating
Frequency-resolved_optical_gating
Number of values in the final calculation of a statistic that are free to vary
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
Experiment methodology
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model
A/B_testing
1969 law by Waldo Tobler
foundation of the fundamental concepts of spatial dependence and spatial autocorrelation and is utilized specifically for the inverse distance weighting method
Tobler's first law of geography
Tobler's_first_law_of_geography
Statistical property
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
System to capture, manage, and present geographic data
terrain. Interpolation is a justified measurement because of a spatial autocorrelation principle that recognizes that data collected at any position will
Geographic_information_system
Variations in data at specific regular intervals less than a year
if the period is not known, the autocorrelation plot can help. If there is significant seasonality, the autocorrelation plot should show spikes at lags
Seasonality
} (ii) for all m ∈ N + {\displaystyle m\in \mathbb {N} ^{+}} , the autocorrelation functions r {\displaystyle r} and r ( m ) {\displaystyle r^{(m)}} of
Self-similar_process
Apparent lack of pattern or predictability in events
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model
Randomness
Condition in which the value of a measurement or observation is only partially known
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model
Censoring_(statistics)
Statistical hypothesis test for the presence of serial correlation
Breusch and Leslie G. Godfrey. The Breusch–Godfrey test is a test for autocorrelation in the errors in a regression model. It makes use of the residuals
Breusch–Godfrey_test
Changing the speed or duration of an audio signal without affecting its pitch
some pitch detection algorithm (commonly the peak of the signal's autocorrelation, or sometimes cepstral processing), and crossfade one period into another
Audio time stretching and pitch scaling
Audio_time_stretching_and_pitch_scaling
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model
List_of_statistical_tests
Measure of statistical dispersion
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model
Interquartile_range
Mathematical transform that expresses a function of time as a function of frequency
signals to instead take the Fourier transform of its autocorrelation function. The autocorrelation function R of a function f is defined by R f ( τ ) =
Fourier_transform
Series of questions for gathering information
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model
Questionnaire
Australian economist (born 1953)
after Breusch and Leslie G. Godfrey, which can be used to identify autocorrelation in the errors of a regression model. Australian Finance Conference
Trevor_S._Breusch
Signal with properties that vary cyclically with time
that exhibits cyclostationarity in second-order statistics (e.g., the autocorrelation function). These are called wide-sense cyclostationary signals, and
Cyclostationary_process
Type of signal in signal processing
n ) ] = 0 {\displaystyle \operatorname {E} [W(n)]=0} , and if its autocorrelation function R W ( n ) = E [ W ( k + n ) W ( k ) ] {\displaystyle
White_noise
Algorithm to estimate signal frequency
ASMDF (Average Squared Mean Difference Function), and other similar autocorrelation algorithms work this way. These algorithms can give quite accurate
Pitch_detection_algorithm
Statistical distribution for dependence between random variables
1016/j.solener.2016.12.022. Munkhammar, J.; Widén, J. (2017). "An autocorrelation-based copula model for generating realistic clear-sky index time-series"
Copula_(statistics)
Measure of joint variability in statistics
{\displaystyle (f\star g)[n]=({\overline {f[-k]}}*g[k])[n]} . Autocovariance Autocorrelation Correlation Convolution Cross-correlation Kun Il Park, Fundamentals
Cross-covariance
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