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Multicollinearity, autocorrelation, and ridge regression

University of British Columbia

The presence of multicollinearity can induce large variances in the ordinary Least-squares estimates of repression coefficients. It has been shown that ridge regression can reduce this adverse effect on estimation. The presence of serially correlated error terms can also cause serious estimation problems. Various two-stage methods, have been proposed to obtain good estimates of the regression coefficients in this case. Although the multicollinearity and autocorrelation problems have long been recognized in regression analysis, they are usually dealt with separately. This thesis explores the joint effects of these two conditions on the mean square error properties of the ordinary ridge estimator as well as the ordinary least-squares estimator. We show that ridge regression is doubly advantageous when multicollinearity is accompanied by autocorrelation in both,the errors and the principal components. We then derive a new ridge type estimator that is adjusted for autocorrelation. Finally, using simulation experiments with different degrees of multicollinearity and autocorrelation, we compare the mean square error properties of various estimators.

Text

2010-03-13

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http://hdl.handle.net/2429/21865

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University of British Columbia

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