Question

Explain what is meant by autocorrelation of regression residuals and detail what estimation problems it causes. How could you detect and solve the residual autocorrelation problem?

Answer 1

The main problem in time series regression is autocorrelation. It is also known as serial correlation. It occurs due to the correlation of the error term observations in a regression. To check for autocorrelation we generally use the error term observations or residuals e. This we can see only afte the estimation of the model and they differ with each data set which is used to estimate the same regression.

The common type of auro correlationis first order autocorrelation which is present when an observed error tends to be influenced by the observed error that immediately precedes it in the previous time period. In this, only one time period separates the two correlated error term observations.

Autocorrelation is a problem because the presence of autocorrelation states that the useful information is missing from the model.

Estimation of autocorrelation

1. It leaves the coefficient estimates unbiased.

2. Increases the variance of the coefficient estimates.

3. Estimated standard errors given by ordinary least squares will be smaller than the true values.

Test to detect and solve autocorrelation- The Durbin Watson Statistic provides a test for autocorrelation, but for only ffirst order autocorrelation only. It ranges from 0 to 4. The closer the Durbin-Watson statistic is to 0, the more likely positive first order autocorrelation is present. The closer it is to 2, the more likely there is no autocorrelation, the closer it is to 4, the more likely negative first order autocorrelation is present.

Treating the autocorrelation-

1. Eliminating the symptoms of autocorrelation by using an estimation method other than ordinary least squares.

2. Prevent autocorrelation from occuring in the first place