Autocorrelation

Autocorrelation measures how correlated a time series is with a delayed, or lagged, copy of itself. Computing the correlation between the series and its value one period earlier gives the lag-1 autocorrelation; repeating this at increasing lags produces an autocorrelation function that shows which past periods still relate to the present one.

A series with strong autocorrelation at lag 7, for instance, has a value each day that tends to resemble the value from a week earlier, a sign of weekly seasonality. This differs from ordinary correlation between two separate variables: autocorrelation is a series' relationship with itself across time, and it is a required diagnostic before fitting models like ARIMA, which explicitly rely on the structure autocorrelation reveals. It is also closely tied to stationarity: many statistical tests and models assume a series' statistical properties, including its autocorrelation structure, do not change over time.

Autocorrelation matters for choosing model structure in time series forecasting, for detecting seasonal cycles before smoothing them with a moving average, and for spotting when residuals from a fitted model still contain a pattern the model missed. A common pitfall is misreading autocorrelation at a business-relevant lag as causal repetition, when it can also arise from a shared external driver, such as a weekly billing cycle, that affects the series without one period truly causing the next.