It is the correlation of a signal with a delayed copy of itself, as a function of the delay (lag).
Card 1 of 259. Answer: It is the correlation of a signal with a delayed copy of itself, as a function of the delay (lag).
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Autocorrelation is the correlation between a series and a lagged copy of itself, as a function of the lag. The lag-k autocorrelation compares each yₜ with yₜ₋ₖ: rₖ = Σ (yₜ − ȳ)(yₜ₋ₖ − ȳ) / Σ (yₜ − ȳ)². It is also called serial correlation, and plotting rₖ against k gives the autocorrelation function, or ACF.
Monthly temperatures in a city show strong positive autocorrelation at lag 12, since January resembles last January, and strong negative autocorrelation at lag 6, January against July. The ACF of daily retail sales often spikes at lag 7, a weekly cycle. For white noise, about 95% of sample autocorrelations fall within ±2/√n, the dashed bands on an ACF plot.
In practice, ACF and partial ACF plots guide the choice of ARIMA orders. Autocorrelated regression residuals break the independence assumption, so standard errors usually come out too small and p-values too optimistic; the Durbin-Watson and Ljung-Box tests check for this. It is also why a random train-test split leaks information in time series.
