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Park test

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In econometrics, the Park test is a test for heteroscedasticity. The test is based on the method proposed by Rolla Edward Park for estimating linear regression parameters in the presence of heteroscedastic error terms.[1]

Background

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In regression analysis, heteroscedasticity refers to unequal variances of the random error terms , such that

.

It is assumed that . The above variance varies with , or the trial in an experiment or the case or observation in a dataset. Equivalently, heteroscedasticity refers to unequal conditional variances in the response variables , such that

,

again a value that depends on – or, more specifically, a value that is conditional on the values of one or more of the regressors . Homoscedasticity, one of the basic Gauss–Markov assumptions of ordinary least squares linear regression modeling, refers to equal variance in the random error terms regardless of the trial or observation, such that

, a constant.

Test description

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Park, on noting a standard recommendation of assuming proportionality between error term variance and the square of the regressor, suggested instead that analysts 'assume a structure for the variance of the error term' and suggested one such structure:[1]

in which the error terms are considered well behaved.

This relationship is used as the basis for this test.

The modeler first runs the unadjusted regression

where the latter contains p − 1 regressors, and then squares and takes the natural logarithm of each of the residuals (), which serve as estimators of the . The squared residuals in turn estimate .

If, then, in a regression of on the natural logarithm of one or more of the regressors , we arrive at statistical significance for non-zero values on one or more of the , we reveal a connection between the residuals and the regressors. We reject the null hypothesis of homoscedasticity and conclude that heteroscedasticity is present.

See also

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Notes

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The test has been discussed in econometrics textbooks.[2][3] Stephen Goldfeld and Richard E. Quandt raise concerns about the assumed structure, cautioning that the vi may be heteroscedastic and otherwise violate assumptions of ordinary least squares regression.[4]

Notes

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  1. ^ a b Park, R. E. (1966). "Estimation with Heteroscedastic Error Terms". Econometrica. 34 (4): 888. JSTOR 1910108.
  2. ^ Gujarati, Damodar (1988). Basic Econometrics (2nd ed.). New York: McGraw–Hill. pp. 329–330. ISBN 0-07-100446-7.
  3. ^ Studenmund, A. H. (2001). Using Econometrics: A Practical Guide (Fourth ed.). Boston: Addison-Wesley. pp. 356–358. ISBN 0-321-06481-X.
  4. ^ Goldfeld, Stephen M.; Quandt, Richard E. (1972) Nonlinear Methods in Econometrics, Amsterdam: North Holland Publishing Company, pp. 93–94. Referred to in: Gujarati, Damodar (1988) Basic Econometrics (2nd Edition), New York: McGraw-Hill, p. 329.