# bgtest

##### Breusch-Godfrey Test

`bgtest`

performs the Breusch-Godfrey test for higher-order
serial correlation.

- Keywords
- htest

##### Usage

```
bgtest(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

`bgtest`

is called from.- fill
starting values for the lagged residuals in the auxiliary regression. By default

`0`

but can also be set to`NA`

.

##### 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.

`bgtest`

also returns the coefficients and estimated covariance
matrix from the auxiliary regression that includes the lagged residuals.
Hence, `coeftest`

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.)

##### Value

A list with class `"bgtest"`

inheriting from `"htest"`

containing the
following components:

the value of the test statistic.

the p-value of the test.

degrees of freedom.

a character string indicating what type of test was performed.

a character string giving the name(s) of the data.

coefficient estimates from the auxiliary regression.

corresponding covariance matrix estimate.

##### References

Breusch, T.S. (1978): Testing for Autocorrelation in Dynamic Linear
Models, *Australian Economic Papers*, 17, 334-355.

Godfrey, L.G. (1978): Testing Against General Autoregressive and
Moving Average Error Models when the Regressors Include Lagged
Dependent Variables', *Econometrica*, 46, 1293-1301.

Wooldridge, J.M. (2013): *Introductory Econometrics: A Modern Approach*,
5th edition, South-Western College.

##### See Also

##### Examples

`library(lmtest)`

```
# NOT RUN {
## 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:
bgtest(y1 ~ x)
## or for fourth-order serial correlation
bgtest(y1 ~ x, order = 4)
## Compare with Durbin-Watson test results:
dwtest(y1 ~ x)
y2 <- filter(y1, 0.5, method = "recursive")
bgtest(y2 ~ x)
bg4 <- bgtest(y2 ~ x, order = 4)
bg4
coeftest(bg4)
# }
```

*Documentation reproduced from package lmtest, version 0.9-35, License: GPL-2 | GPL-3*