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.