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Everything about Autocorrelation
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. Essentially, it quantifies the similarity between observations of a random variable at different points in its domain. The analysis of autocorrelation is a mathematical tool for identifying repeating patterns or hidden periodicities within a signal obscured by noise. Autocorrelation is widely used in signal processing, time domain and time series analysis to understand the behavior of data over time. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: AutocorrelationA 5-minute orientation
- Skim a recent paper: Spatial autocorrelation in land use type and ecosystem service value in Hainan Tropical Rain Forest National ParkInfluential work since 2022
- Pick up a classic book: Trend analysis techniquesThe most-reprinted book on the subject
- Read the landmark paper: A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance MatrixCited 16,072 times
- Go sideways: Cross-correlationA closely related topic
- Go sideways: Stationary processA closely related topic
📖 Definitions
Noun The cross-correlation of a signal with itself: the correlation between values of a signal in successive time periods.
🏆 Landmark papers (most cited)
A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix
Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation
Local Spatial Autocorrelation Statistics: Distributional Issues and an Application
Spatial Autocorrelation: Trouble or New Paradigm?
Methods to account for spatial autocorrelation in the analysis of species distributional data: a review
Temporal Autocorrelation in Univariate Linear Modeling of FMRI Data
The influence of autocorrelation on the ability to detect trend in hydrological series
g_wham—A Free Weighted Histogram Analysis Implementation Including Robust Error and Autocorrelation Estimates
🆕 Influential since 2022
Spatial autocorrelation in land use type and ecosystem service value in Hainan Tropical Rain Forest National Park
Spatial autocorrelation equation based on Moran’s index
A spatial autocorrelation analysis of road traffic crash by severity using Moran’s I spatial statistics: A comparative study of Addis Ababa and Berlin cities
Water ecological security assessment and spatial autocorrelation analysis of prefectural regions involved in the Yellow River Basin
Fair train-test split in machine learning: Mitigating spatial autocorrelation for improved prediction accuracy
📚 Books worth reading
- 📕Trend analysis techniques · 1990
Habits and autocorrelation in the almost ideal demand system applied to foodLaura Blanciforti · 1984- 📕Expected value and variance of Moran's bivariate spatial autocorrelation statistic for a permutation testRaymond L. Czaplewski · 1993
- 📕An overdetermined system for improved autocorrelation based spectral moment estimator performanceByron M. Keel · 1996
- 📕Digital PIV (DPIV) software analysis systemJames L. Blackshire · 1997
- 📕Vektorautokorrelationen stochastischer Prozesse und die Spezifikation von ARMA-ModellenEfstathios Paparoditis · 1990
Spatial autocorrelationA. D. Cliff · 1973
Expected value and variance of Moran's bivariate spatial autocorrelation statistic for a permutation testR.L. Czaplewski · 1993
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Cross-correlation In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is…
- Stationary process In mathematics and statistics, a stationary process (also called a strict/strictly stationary process or strong/strongly stationary process) is a stochastic…
- Cross-covariance In probability and statistics, given two stochastic processes {Xt} and {Yt}, the cross-covariance is a function that gives the covariance of one process…
- Autocovariance In probability theory and statistics, given a stochastic process, the autocovariance is a function that gives the covariance of the process with itself…
- Correlogram In the analysis of data, a correlogram is a chart of correlation statistics. For example, in time series analysis, a plot of the sample autocorrelations…
- Autoregressive model In statistics, an autoregressive (AR) model is a modelled representation of a type of random process. It can be used to describe time-varying processes…
- Whittaker–Shannon interpolation formula The Whittaker–Shannon interpolation formula or sinc interpolation is a method to construct a continuous-time bandlimited function from a sequence of real…
- Wiener–Khinchin theorem In applied mathematics and statistics, the Wiener–Khinchin theorem or Wiener–Khintchine theorem, also known as the Wiener–Khinchin–Einstein theorem or…