com.numericalmethod.suanshu.stats.test.regression.linear.heteroskedasticity
Class White

java.lang.Object
  com.numericalmethod.suanshu.stats.test.HypothesisTest
      com.numericalmethod.suanshu.stats.test.regression.linear.heteroskedasticity.White

public class White
extends HypothesisTest

The White test is used to test for heteroskedasticity in a linear regression model. It tests whether the estimated variance of the residuals from a regression are dependent on the values of the independent variables (regressors).

The White test tests for conditional heteroskedasticity. It is a chi-squared test: the test statistic is nχ² with k degrees of freedom. If the White test shows that there is conditional heteroskedasticity, we can consider a GARCH model.

See Also:

• White, H. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica 48 (4): 817–838. MR575027 JSTOR 1912934. 1980.
• R. Koenker. "A Note on Studentizing a Test for Heteroskedasticity," Journal of Econometrics 17, 107–112. 1981.
• Wikipedia: White test

Field Summary

protected int	n number of observations
protected Residuals	residuals

Fields inherited from class com.numericalmethod.suanshu.stats.test.HypothesisTest

k, N, pValue, testStatistics

Constructor Summary

White(Residuals residuals)
Perform the White test to test for heteroskedasticity in a linear regression model.

Method Summary

java.lang.String	alternativeHypothesis() Get a description of the alternative hypothesis.
protected OlsRegression	auxiliaryOlsRegression(Vector y, Residuals residuals) the auxiliary regression
protected OlsRegression	getAuxiliaryRegression()
protected ChiSquareDistribution	getX2()
java.lang.String	nullHypothesis() Get a description of the null hypothesis.
double	pValue() Get the p-value.
double	testStatistics() Get the test statistics.

Methods inherited from class com.numericalmethod.suanshu.stats.test.HypothesisTest

oneSidedPvalue, rejectNull

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

residuals

protected final Residuals residuals

n

protected final int n

number of observations

Constructor Detail

White

public White(Residuals residuals)

Perform the White test to test for heteroskedasticity in a linear regression model.

Parameters:

residuals - the Residuals object from an OLS regression

Method Detail

testStatistics

public double testStatistics()

Description copied from class: HypothesisTest

Get the test statistics.

Returns:

the test statistics

See Also:

Wikipedia: Test statistic

getX2

protected ChiSquareDistribution getX2()

getAuxiliaryRegression

protected OlsRegression getAuxiliaryRegression()

auxiliaryOlsRegression

protected OlsRegression auxiliaryOlsRegression(Vector y,
                                               Residuals residuals)

the auxiliary regression

Returns:

the auxiliary regression

nullHypothesis

public java.lang.String nullHypothesis()

Description copied from class: HypothesisTest

Get a description of the null hypothesis.

Specified by:

nullHypothesis in class HypothesisTest

Returns:

the null hypothesis description

See Also:

Wikipedia: Null hypothesis

alternativeHypothesis

public java.lang.String alternativeHypothesis()

Description copied from class: HypothesisTest

Get a description of the alternative hypothesis.

Specified by:

alternativeHypothesis in class HypothesisTest

Returns:

the alternative hypothesis description

See Also:

Wikipedia: Alternative hypothesis

pValue

public double pValue()

Description copied from class: HypothesisTest

Get the p-value.

Overrides:

pValue in class HypothesisTest

Returns:

the p-value

See Also:

Wikipedia: P-value