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
)

Arguments

formula: a symbolic description for the model to be tested (or a fitted "lm" object).
order: integer. maximal order of serial correlation to be tested.
order.by: Either a vector z or a formula with a single explanatory variable like ~ z. The observations in the model are ordered by the size of z. If set to NULL (the default) the observations are assumed to be ordered (e.g., a time series).
type: the type of test statistic to be returned. Either "Chisq" for the Chi-squared test statistic or "F" for the F test statistic.
data: an optional data frame containing the variables in the model. By default the variables are taken from the environment which BreuschGodfreyTest is called from.
fill: starting values for the lagged residuals in the auxiliary regression. By default 0 but can also be set to NA.

Value

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.

Details

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.)

Note

This function was previously published as bgtest in the lmtest package and has been integrated here without logical changes.

References

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.

Author

David Mitchell david.mitchell@dotars.gov.au, Achim Zeileis

Examples


## 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)
#> 
#> 	Breusch-Godfrey test for serial correlation of order up to 1
#> 
#> data:  y1 ~ x
#> LM test = 0.67455, df = 1, p-value = 0.4115
#> 

## or for fourth-order serial correlation
BreuschGodfreyTest(y1 ~ x, order = 4)
#> 
#> 	Breusch-Godfrey test for serial correlation of order up to 4
#> 
#> data:  y1 ~ x
#> LM test = 2.6692, df = 4, p-value = 0.6146
#> 

## Compare with Durbin-Watson test results:
DurbinWatsonTest(y1 ~ x)
#> 
#> 	Durbin-Watson test
#> 
#> data:  y1 ~ x
#> DW = 2.0564, p-value = 0.6502
#> alternative hypothesis: true autocorrelation is greater than 0
#> 

y2 <- stats::filter(y1, 0.5, method = "recursive")
BreuschGodfreyTest(y2 ~ x)
#> 
#> 	Breusch-Godfrey test for serial correlation of order up to 1
#> 
#> data:  y2 ~ x
#> LM test = 16.451, df = 1, p-value = 0.00004992
#>