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

All Implemented Interfaces:

java.io.Serializable

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

, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
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

Constructors

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

Method Summary

Modifier and Type	Method and Description
java.lang.String	getAlternativeHypothesis() Get a description of the alternative hypothesis.
protected OLSRegression	getAuxiliaryOLSRegression(Vector y, Residuals residuals) the auxiliary regression
protected OLSRegression	getAuxiliaryRegression()
java.lang.String	getNullHypothesis() Get a description of the null hypothesis.
protected ChiSquareDistribution	getX2()
double	pValue() Get the p-value.
double	statistics() Get the test statistics.

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

isNullRejected, oneSidedPvalue

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

statistics

public double statistics()

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()

getAuxiliaryOLSRegression

protected OLSRegression getAuxiliaryOLSRegression(Vector y,
                                                  Residuals residuals)

the auxiliary regression

Returns:

the auxiliary regression

getNullHypothesis

public java.lang.String getNullHypothesis()

Description copied from class: HypothesisTest

Get a description of the null hypothesis.

Specified by:

getNullHypothesis in class HypothesisTest

Returns:

the null hypothesis description

See Also:

Wikipedia: Null hypothesis

getAlternativeHypothesis

public java.lang.String getAlternativeHypothesis()

Description copied from class: HypothesisTest

Get a description of the alternative hypothesis.

Specified by:

getAlternativeHypothesis 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