SystemResults.breusch_pagan() WaldTestStatistic | InvalidTestStatistic[source]

Breusch-Pagan LM test for no cross-correlation


Test statistic for null all correlations are zero.

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The null hypothesis is that the shock correlations are all 0, and so there are no gains to using GLS estimation in the system estimator. When the null is rejected, there should be efficiency gains to using GLS as long the regressors are not common to all models.

The Breusch-Pagan test statistic is defined as

\[LM = n \sum_{i=1}^k \sum_{j=i+1}^k \hat{\rho}_{ij}^2\]

where \(\hat{\rho}_{ij}\) is the sample residual correlation between series i and j. n is the sample size. It has an asymptotic \(\chi^2_{k(k-1)/2}\) distribution. See [1] for details.