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] In regression analysis, heteroscedasticity refers to unequal variances of the random error terms
case or observation in a dataset.
Equivalently, heteroscedasticity refers to unequal conditional variances in the response variables
– 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 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
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
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.
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.