Breusch-Godfrey test (BG Test)

Keith Tan, CFA


The Breusch-Godfrey test is a statistical test that is used to detect autocorrelation in the residuals of a linear regression model. It helps to detect autocorrelation at different lags and it’s applicable to both linear and non-linear models.

The test starts with an initial regression where we record down all the residuals for each time period. The residual terms are then regressed against the original set of independent variables, plus one or more additional variables representing lagged residuals. For example, we have lagged residuals for time T-1, and T-2 to test for serial correlation with 1 and 2 time lag respectively, and P1 and P2 are their coefficients. For each of these coefficients, we perform hypothesis tests on whether they are significantly different from zero, with an assumed Chi-square distribution and the degrees of freedom of p-k-1. The F-statistic is provided with most statistical software, so you just need to check it against the critical value. If we reject H-not for a particular time lag, we conclude that there is serial correlation present for that time lag.

Compare: Durbin-Watson Test

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