INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 104 There seems to be no limit to the different possible
types of heteroscedasticity, and consequently, a large number of different tests appropriate for different conditions have been suggested. The attention here would, however,be focused on three tests that hypothesize a relationship between the variance of the disturbance term and the size of the explanatory variables. These would be
the Spearman rank correlation, Goldfeld–
Quandt, and Glejser tests.
3.1.3.4 The Spearman Rank Correlation Test This test assumes that the variance of the disturbance term is either increasing or decreasing as
Xincreases and that there will be a correlation between the absolute size of
the residuals and the size of Xin an OLS regression. The data on
Xand the absolute values of the residuals are both ranked, and the rank correlation
coefficient is defined as ∑
(
)
…[3.02] where
Diis the difference between the rank of
Xand the rank of
ein
observation i. Under the assumption that the population correlation coefficient is 0, the rank correlation coefficient has a normal distribution with 0 mean and variance
1
(
1)
n
in large samples. Theappropriate test statistic is therefore
√ and the null hypothesis of homoscedasticity will be rejected at the 5 percent level if its absolute value is greater than 1.96 and at the 1 percent level if its absolute value is greater than 2.58, using two- tailed tests. If there is more than one explanatory
variable in the model, the test maybe performed with anyone of them.
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