Glossary

Autocorrelation

Autocorrelation measures the degree of similarity between observations as a function of the lag separating them in time or space. A positively autocorrelated series exhibits values that are more alike when they are close together than when far apart. Autocorrelation is central...

Definition

Autocorrelation measures the degree of similarity between observations as a function of the lag separating them in time or space. A positively autocorrelated series exhibits values that are more alike when they are close together than when far apart. Autocorrelation is central to time-series analysis: it informs the choice of ARMA lag orders, violates the classical OLS assumption of independent errors, and must be accounted for in bootstrap procedures for dependent data.

Why It Matters

Ignoring autocorrelation in regression residuals leads to inefficient estimates and invalid standard errors, which in turn distort hypothesis tests and confidence intervals. Detecting and modelling autocorrelation is essential for reliable inference in any time-series study, from macroeconomic forecasting to financial risk modelling. Moreover, autocorrelation patterns reveal the memory structure of a series, guiding model selection.

Example

Monthly Turkish inflation data often show strong first-order autocorrelation: a high inflation month is likely followed by another high month. The autocorrelation function (ACF) shows a significant spike at lag 1 that decays slowly, suggesting an AR(1) or ARMA process rather than white noise.

Related Terms

Software Notes

  • SPSS: Analyze > Forecasting > Autocorrelations; select the variable and number of lags to display ACF and PACF plots.
  • R: Use acf() and pacf() for autocorrelation and partial autocorrelation plots. The Box.test() function performs the Ljung-Box test for residual autocorrelation.
  • Stata: Use corrgram variable to display ACF and PACF. Use estat bgodfrey after regression for the Breusch-Godfrey test against autocorrelation.