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The Breusch–Godfrey 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. [3]
The Breusch–Godfrey test is named after him and Trevor S. Breusch. [1] He is an emeritus professor of econometrics at the University of York . He is the author of "Misspecification tests in econometrics: the Lagrange multiplier principle and other approaches" [ 2 ] and "Bootstrap Tests for Regression Models".
Stata: the command estat dwatson, following regress in time series data. [6] Engle's LM test for autoregressive conditional heteroskedasticity (ARCH), a test for time-dependent volatility, the Breusch–Godfrey test, and Durbin's alternative test for serial correlation are also available.
In Stata, one specifies the full regression, and then enters the command estat hettest followed by all independent variables. [9] [10] In SAS, Breusch–Pagan can be obtained using the Proc Model option. In Python, there is a method het_breuschpagan in statsmodels.stats.diagnostic (the statsmodels package) for Breusch–Pagan test. [11]
ADF-GLS test; Unit root tests are closely linked to serial correlation tests. However, while all processes with a unit root will exhibit serial correlation, not all serially correlated time series will have a unit root. Popular serial correlation tests include: Breusch–Godfrey test; Ljung–Box test; Durbin–Watson test
The null hypothesis of this chi-squared test is homoscedasticity, and the alternative hypothesis would indicate heteroscedasticity. Since the Breusch–Pagan test is sensitive to departures from normality or small sample sizes, the Koenker–Bassett or 'generalized Breusch–Pagan' test is commonly used instead.
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White test is a statistical test that establishes whether the variance of the errors in a regression model is constant: that is for homoskedasticity. This test, and an estimator for heteroscedasticity-consistent standard errors , were proposed by Halbert White in 1980. [ 1 ]