What are the Consequences of Autocorrelation (2020)

Autocorrelation, when ignored, can lead to several issues in analyzing data, particularly in statistical models. In this post, we will discuss some important consequences of the existence of autocorrelation in the data. The consequences of the OLS estimators in the presence of Autocorrelation can be summarized as follows:

Consequences Patterns of Autocorrelation and Non-Autocorrelation

Consequences of Autocorrelation on OLS Estimators If Exists

When the disturbance terms are serially correlated then the OLS estimators of the $\hat{\beta}$s are still unbiased and consistent but the optimist property (minimum variance property) is not satisfied. This makes it harder to determine if the estimated effect of a variable is truly significant.
The OLS estimators will be inefficient and therefore, no longer BLUE. Inefficient means there could be better ways to estimate the model parameters that would produce more precise results with lower variance.
The estimated variance of the regression coefficients will be biased and inconsistent and will be greater than the variances of estimate calculated by other methods, therefore, hypothesis testing is no longer valid. In most of the cases, $R^2$ will be overestimated (indicating a better fit than the one that truly exists). The t- and F-statistics will tend to be higher. One might reject a true null hypothesis (meaning a relationship does not exist) or fail to reject a false one (meaning a relationship appears to exist when it does not).
The variance of random term $u$ may be under-estimated if the $u$’s are autocorrelated. That is, the random variance $\hat{\sigma}^2=\frac{\sum \hat{u}_i^2}{n-2}$ is likely to be under-estimate the true $\sigma^2$.
Among the consequences of autocorrelation, another is, that if the disturbance terms are autocorrelated then the OLS estimates are not asymptotic. That is $\hat{\beta}$s are not asymptotically efficient.

Therefore, autocorrelation may lead to misleading results and unreliable statistical tests. If autocorrelation is suspected in the data being analyzed, then use different statistical techniques to address it and improve the validity of your analysis.