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The problems of heteroscedasticity and autocorrelation of residuals can occur because of misspecificaiion of a regression model...before doing anything, make sure that the model is correctly specified...ARCH models can simultaneously make corrections for both heter-oscedasicity and autocorrelation.
In a recent article in this journal, Wang and Akabay (W & A) discuss the problems associated with the detection and elimination of heteroscedastic error terms. Normally heteroscedasticity is a problem in cross sectional data, but it can be a problem in time series data, particularly when there has been a substantial increase or decrease in the value of the dependent variable in a short time interval, causing the regression variance to increase or decrease. Wang and Akabay's first example involves time series data, and they provide the data that are used in the analysis in their article.
In order to generate unbiased regression results, using ordinary least squares (OLS), the error terms must be normally distributed, thus uncorrelated either to any of the independent variables or to themselves with any lag. In the first case, the issue of heteroscedasticity is being addressed; in the second, autocorrelation. W & A consider only the first issue in their article since their intent is to demonstrate the corrections tat are necessary to mitigate the effects of heteroscedasticity. In a subsequent article, the same authors demonstrate the correction techniques for autocorrelation.
Normal practice, in examining errors for heteroscedasticity, is to plot the errors against the independent variables and to perform a Goldfeld-Quandt, Spearman, Glejser, Park, Likelihood ratio, or Breusch and Pagan test. Normal practice, in the case of autocorrelation, is to examine the correlation of the error term u sub t with u sub t-a using the Durbin-Watson test or Theil U Statistic (for regressions with lagged dependent variables). Adjoining error terms are used (a = 1) since, in the case presented, the data are annual and have no seasonality. If seasonality exists in the data, the model should include a set of seasonal variables to "explain" the seasonality pattern in the dependent variable.
One of the key issues is how to proceed if both problems occur simultaneously in the data and are reflected in the OLS regression results. A second key issue is the evaluation of the regression equation...