Correlation function measurement

Correlation function measurement estimates how variables co-vary across observations, spatial separations, or time lags. It summarizes dependence at specified separations rather than describing only overall association.

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Pearson correlation coefficient: A standardized measure of linear association between two variables. At zero lag, this coefficient is the simplest estimate of pairwise co-variation.
Random variable: A variable whose possible values are described by a probability distribution. Correlation functions describe dependence among random variables indexed across observations or positions.
Time-series analysis: Statistical analysis of observations indexed in time. Autocorrelation helps identify persistence, cycles, and suitable time-series models.
Mutual information: A measure of statistical dependence based on reduction in uncertainty about one variable from another. Unlike correlation, it can detect many nonlinear dependencies.
Autocorrelation: Correlation between values of the same process separated by a time or spatial lag. It measures how a signal resembles delayed or displaced copies of itself.
Expectation: The probability-weighted average value of a random variable. The theoretical correlation is defined using means and expected products.
Spatial statistics: Statistical methods for data whose locations or spatial relationships matter. Spatial correlation quantifies how similarity changes with distance.
Spearman's rank correlation coefficient: A correlation measure computed from ranks, capturing monotonic association. Rank-based estimates resist some outliers and do not require linear association.
Cross-correlation: Correlation between two signals as a function of their relative time or spatial displacement. Lag-dependent cross-correlation reveals offsets and shared structure between variables.
Stationary process: A stochastic process whose statistical properties are invariant under shifts in its index. Stationarity lets temporal correlation depend on lag rather than absolute time.