Breusch-Godfrey Test
Testing Autocorrelation in Residuals
Nimesh Mani Risal
Introduction
● The Breusch-Godfrey test assesses whether there is
autocorrelation in regression residuals
● It examines the joint significance of lagged residuals to
validate the absence of autocorrelation up to a specified
order in time series data.
Model Assumption
Suppose we want to estimate the following model
Yt = β1 + β2Xt + µt
…………………………………… (1)
Assume the error term follows the pth-order autoregressive,
AR(p), scheme as follows:
µt =ρ1 µt-1 + ρ2 µt-2 +……. +ρ µt-p ……………………. (2)
Procedure
Step I : Estimate eq. 1 and obtain the residuals, µt
Step II : Regress µt on the original Xt and µt-1 , µt-2 ………., µt-p and obtain R2
µt = β1 + β2Xt + ρ1 µt-1 + ρ2 µt-2 +……. +ρ µt-p + êt
Step III :
Either compute the F test for the joint significance of the residuals
Or,Compute LM = (n-p) R2aux ~ ꭙp2
Where,
n = number of observations
P = number of periods (lags)
µt-1……, µt-p
Decision Rule
● In case of F test, F > Fcritical reject hypothesis of
autocorrelation and vice versa
Or,
● If the computed ꭙ2 > ꭙ2critical reject the hypothesis of no
autocorrelation (null hypothesis) and vice versa.
Limitations
● The value of p (lag value) cannot be specified earlier
● The test assumes that the data has no heteroskedasticity
Test Performed in Stata
Thank you