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Breusch–Godfrey test
In statistics, the Breusch–Godfrey test, named after Trevor S. Breusch and Leslie G. Godfrey, is used to assess the validity of some of the modelling assumptions inherent in applying regression-like models to observed data series. In particular, it tests for the presence of serial dependence 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 are obtained if it is not taken into account. 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. This type of structure is common in econometric models. A similar assessment can be also carried out with the Durbin–Watson test.
Because the test is based on the idea of Lagrange multiplier testing, it is sometimes referred to as LM test for serial correlation.
==Background==
The Breusch–Godfrey serial correlation LM test is a test for autocorrelation in the errors in a regression model. It makes use of the residuals from the model being considered in a regression analysis, and a test statistic is derived from these. The null hypothesis is that there is no serial correlation of any order up to ''p''.〔(Macrodados 6.3 Help – Econometric Tools )〕
The test is more general than 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. The BG test has none of these restrictions, and is statistically more powerful than Durbin's ''h'' statistic.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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