Autocorrelation

Autocorrelation measures how strongly a variable’s values are related to its own values separated by a time lag. It describes dependence across observations in a sequence.

Time series: A sequence of observations indexed by time or another ordered dimension. Autocorrelation measures dependence between observations at different positions in a time series.
Autoregressive model: A time-series model that predicts values from weighted combinations of earlier values. Autocorrelation patterns help identify and estimate dependence on past observations.
Pearson correlation coefficient: A normalized measure of linear association between two variables. Autocorrelation applies correlation to a series and a lagged copy of itself.
Cross-correlation: A measure of similarity between two signals as one is shifted relative to the other. It compares different series, whereas autocorrelation compares a series with itself.
Lag operator: An operator that shifts a time series backward or forward by a specified number of observations. Applying a lag operator pairs each value with an earlier value for autocorrelation.
Box–Jenkins method: A systematic approach to fitting autoregressive integrated moving-average models to time series. Its model-identification stage uses autocorrelation and partial autocorrelation plots.
Stationary process: A stochastic process whose relevant statistical properties do not change under time shifts. For a stationary process, autocorrelation depends on lag rather than absolute time.
Spurious correlation: An apparent statistical association produced by confounding, shared trends, or other noncausal structure. Trending series can show strong autocorrelation and misleading associations without direct connection.
Autocovariance: The covariance between a stochastic process and a time-shifted version of itself. Autocorrelation is autocovariance normalized by the process variance.
Ljung–Box test: A statistical test of whether a group of autocorrelations in a time series are jointly zero. It tests whether residuals retain autocorrelation after a time-series model is fitted.

Linked from 7 pages