When autocorrelation is present, which assumption is considered violated?

When autocorrelation is present, the assumption that the error terms are independent is considered violated. Autocorrelation refers to the correlation of a time series with its own past values. In the context of regression analysis, this means that the residuals (errors) from one time period are correlated with the residuals from another time period.

This correlation indicates that the errors are not independent, which violates one of the key Gauss-Markov assumptions necessary for the ordinary least squares (OLS) estimator to be efficient. When this assumption is violated, it can lead to inefficient estimates and can affect statistical tests regarding the significance of the predictors in the model.

Other assumptions, such as homoscedasticity (constant variance of errors) and normality of errors, can still hold even when autocorrelation is present, although these characteristics might also need to be checked in practice. Additionally, the linearity of the relationship refers to the relationship between the independent and dependent variables and is separate from the errors' behavior.