[1][2] In particular, it tests for the presence of serial correlation that has not been included in a proposed model structure and which, if present, would mean that incorrect conclusions would be drawn from other tests or that sub-optimal estimates of model parameters would be obtained.
The regression models to which the test can be applied include cases where lagged values of the dependent variables are used as independent variables in the model's representation for later observations.
The test is named after Trevor S. Breusch and Leslie G. Godfrey.
It makes use of the residuals from the model being considered in a regression analysis, and a test statistic is derived from these.
However, the test is more general than that using the Durbin–Watson statistic (or Durbin's h statistic), which is only valid for nonstochastic regressors and for testing the possibility of a first-order autoregressive model (e.g. AR(1)) for the regression errors.
However, the BG test requires the assumptions of stronger forms of predeterminedness and conditional homoscedasticity.
Consider a linear regression of any form, for example where the errors might follow an AR(p) autoregressive scheme, as follows: The simple regression model is first fitted by ordinary least squares to obtain a set of sample residuals
Breusch and Godfrey[citation needed] proved that, if the following auxiliary regression model is fitted and if the usual Coefficient of determination (
The following asymptotic approximation can be used for the distribution of the test statistic: when the null hypothesis