Autocorrelation
Autocorrelation is the correlation of a variable with its own past values, or of regression residuals across time. In regression it violates the independence assumption, making standard errors unreliable though coefficients remain unbiased.
FrameworkClassical linear regression model
See it move
Autocorrelation occurs when a regression's residuals are correlated with their own past values, most often in time-series data. Positive first-order autocorrelation (ρ₁ > 0) means consecutive errors cluster in the same direction, which understates OLS standard errors and inflates t-statistics. Coefficients remain unbiased, but hypothesis tests built on them become unreliable.
The formula
Variables
- First-order autocorrelation coefficient (ranges from −1 to +1)
- Regression error term at time t
- Regression error term one period earlier
ρ₁ = 0 indicates no first-order autocorrelation. Positive ρ₁ means consecutive errors tend to share the same sign; negative ρ₁ means they alternate.