When autocorrelation of the residuals is present, what effect can this have on interval estimation and significance tests regarding the regression model involved?

Answer 1

Most significance tests and interval estimation methods assume randomly sampled observations.

The presence of autocorrelation in the data means that the observations are not random, but correlated to previous values, typical of time-series related data.

This phenomenon results in null hypotheses indicating the absence of relationships are frequently rejected, for the wrong reason. The presence of an apparent correlation also narrows the estimation intervals and confidence intervals, resulting in a false sense of accuracy of the model.

The statistical test for autocorrelation, the Durbin-Watson test is designed to indicate the presence or absence of autocorrelation. The statistic ranges from 0 (positive autocorrelation) to 4 (negative), 2 meaning absence of autocorrelation.

Answer 2

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