bgtest {lmtest} | R Documentation |

## Breusch-Godfrey Test

### Description

`bgtest`

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

### Usage

bgtest(formula, order = 1, order.by = NULL, type = c("Chisq", "F"), data = list())

### 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. |

### 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
the exact F statistic which, under *H_0*, follows an *F*
distribution with degrees of freedom as given in `parameter`

.

The starting values for the lagged residuals in the supplementary
regression are chosen to be 0.

### Value

A list with class `"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. |

### Author(s)

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

### 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.

### See Also

`dwtest`

### 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:
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)

[Package

*lmtest* version 0.9-14

Index]