Autocorrelation
Summary
Setup:
- The static linear regression model
\[y_t=β_1+β_2x_{t,2}+...+β_kx_{t,k}+ε_t , t=1,…,T\]
- All data is stationary
- The explanatory variables are exogenous
- The error terms are homoscedastic
- The error terms are autocorrelated.
Consequences:
- If the error terms are autocorrelated then the GM assumptions are violated
- The OLS estimator is still unbiased and consistent (under mild conditions).
- The OLS estimator is no longer efficient.
- The OLS GM variance formula is incorrect. Therefore, the OLS standard errors are inconsistent and all inference will be misleading even when \(T\) is large.