What is serial correlation problem?
Serial correlation (also called Autocorrelation) is where error terms in a time series transfer from one period to another. In other words, the error for one time period a is correlated with the error for a subsequent time period.
For example, an underestimate for one quarter’s profits can result in an underestimate of profits for subsequent quarters.
What are the consequence of serial correlation problem?
Consequences of Serial Correlation
Serial correlation will not affect the unbiasedness or consistency of OLS estimators, but it does affect their efficiency. With positive serial correlation, the OLS estimates of the standard errors will be smaller than the true standard errors. This will lead to the conclusion that the parameter estimates are more precise than they really are.
Heteroscedasticity : one of the assumptions made about residuals/errors in OLS regression is that the errors have the same but unknown variance. This is known as constant variance or homoscedasticity. When this assumption is violated, the problem is known as heteroscedasticity.
Consequences of Heteroscedasticity
The OLS estimators and regression predictions based on them remains unbiased and consistent. The OLS estimators are no longer the BLUE (Best Linear Unbiased Estimators) because they are no longer efficient, so the regression predictions will be inefficient too. Because of the inconsistency of the covariance matrix of the estimated regression coefficients, the tests of hypotheses, (t-test, F-test) are no longer valid.
olsrr provides the following 4 tests for detecting heteroscedasticity:
- Bartlett Test
- Breusch Pagan Test
- Score Test
- F Test
Pure versus impure heteroscedasticity
Pure heteroscedasticity refers to cases where you specify the correct model and yet you observe non-constant variance in the residual plots. Impure heteroscedasticity refers to cases where you incorrectly specify the model, and that causes the non-constant variance.