Description Usage Arguments Details Value Note Author(s) References See Also Examples
BreuschGodfreyTest
performs the BreuschGodfrey test for higherorder
serial correlation.
1 2 
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 Chisquared 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 tstatistics 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 pvalue 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, 12931302.
Breusch, T.S. (1979): 'Testing for Autocorrelation in Dynamic Linear Models', Australian Economic Papers, 17, 334355.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  ## Generate a stationary and an AR(1) series
x < rep(c(1, 1), 50)
y1 < 1 + x + rnorm(100)
## Perform BreuschGodfrey test for firstorder serial correlation:
BreuschGodfreyTest(y1 ~ x)
## or for fourthorder serial correlation
BreuschGodfreyTest(y1 ~ x, order = 4)
## Compare with DurbinWatson test results:
DurbinWatsonTest(y1 ~ x)
y2 < filter(y1, 0.5, method = "recursive")
BreuschGodfreyTest(y2 ~ x)

BreuschGodfrey test for serial correlation of order up to 1
data: y1 ~ x
LM test = 0.1479, df = 1, pvalue = 0.7005
BreuschGodfrey test for serial correlation of order up to 4
data: y1 ~ x
LM test = 2.7486, df = 4, pvalue = 0.6007
DurbinWatson test
data: y1 ~ x
DW = 2.0688, pvalue = 0.6731
alternative hypothesis: true autocorrelation is greater than 0
BreuschGodfrey test for serial correlation of order up to 1
data: y2 ~ x
LM test = 17.968, df = 1, pvalue = 2.247e05
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