Autocorrelation

In a time series, observations are often related to earlier ones. Positive autocorrelation means high values tend to follow high values and low values follow low values. Negative autocorrelation means high values tend to follow low values, and vice versa.

For example, monthly unemployment rates are strongly positively autocorrelated: if unemployment is high this month, it is likely to be high next month too. Daily stock returns, by contrast, usually show very little autocorrelation, which is consistent with the idea that past returns cannot easily predict future ones.

Autocorrelation is measured at different lags, such as one period, two periods and so on. Charts of autocorrelation at different lags help analysts identify patterns, such as seasonality, and choose forecasting models.

Autocorrelation matters for statistical analysis. Many standard statistical methods assume observations are independent. If a time series is autocorrelated, these methods can give misleading results, such as overstating confidence in a relationship. It also matters for risk measurement, since autocorrelation in returns can make annualized volatility estimates inaccurate.