Breusch-Godfrey Test
BreuschGodfreyTest performs the Breusch-Godfrey test for higher-order
serial correlation.
BreuschGodfreyTest(formula, order = 1, order.by = NULL, type = c("Chisq", "F"),
data = list(), fill = 0)formula |
a symbolic description for the model to be tested
(or a fitted |
order |
integer. maximal order of serial correlation to be tested. |
order.by |
Either a vector |
type |
the type of test statistic to be returned. Either
|
data |
an optional data frame containing the variables in the
model. By default the variables are taken from the environment
which |
fill |
starting values for the lagged residuals in the auxiliary
regression. By default |
Under H_0 the test statistic is asymptotically Chi-squared with
degrees of freedom as given in parameter.
If type is set to "F" the function returns
a finite sample version of the test statistic, employing an F
distribution with degrees of freedom as given in parameter.
By default, the starting values for the lagged residuals in the auxiliary
regression are chosen to be 0 (as in Godfrey 1978) but could also be
set to NA to omit them.
BreuschGodfreyTest also returns the coefficients and estimated covariance
matrix from the auxiliary regression that includes the lagged residuals.
Hence, CoefTest (package: RegClassTools) can be used to inspect the results. (Note,
however, that standard theory does not always apply to the standard errors
and t-statistics in this regression.)
A list with class "BreuschGodfreyTest" inheriting from "htest" containing the
following components:
statistic |
the value of the test statistic. |
p.value |
the p-value of the test. |
parameter |
degrees of freedom. |
method |
a character string indicating what type of test was performed. |
data.name |
a character string giving the name(s) of the data. |
coefficients |
coefficient estimates from the auxiliary regression. |
vcov |
corresponding covariance matrix estimate. |
This function was previously published as bgtest in the lmtest package and has been integrated here without logical changes.
David Mitchell <david.mitchell@dotars.gov.au>, Achim Zeileis
Johnston, J. (1984): Econometric Methods, Third Edition, McGraw Hill Inc.
Godfrey, L.G. (1978): 'Testing Against General Autoregressive and Moving Average Error Models when the Regressors Include Lagged Dependent Variables', Econometrica, 46, 1293-1302.
Breusch, T.S. (1979): 'Testing for Autocorrelation in Dynamic Linear Models', Australian Economic Papers, 17, 334-355.
## Generate a stationary and an AR(1) series x <- rep(c(1, -1), 50) y1 <- 1 + x + rnorm(100) ## Perform Breusch-Godfrey test for first-order serial correlation: BreuschGodfreyTest(y1 ~ x) ## or for fourth-order serial correlation BreuschGodfreyTest(y1 ~ x, order = 4) ## Compare with Durbin-Watson test results: DurbinWatsonTest(y1 ~ x) y2 <- filter(y1, 0.5, method = "recursive") BreuschGodfreyTest(y2 ~ x)
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