R: Goldfeld-Quandt Test

gqtest {lmtest} | R Documentation

## Goldfeld-Quandt Test

### Description

Goldfeld-Quandt test against heteroskedasticity.

### Usage

    gqtest(formula, point = 0.5, fraction = 0,
      alternative = c("greater", "two.sided", "less"),
      order.by = NULL, data = list())

### Arguments

`formula` | a symbolic description for the model to be tested (or a fitted `"lm"` object).
`point` | numerical. If `point` is smaller than 1 it is interpreted as percentages of data, i.e. `n*point` is taken to be the (potential) breakpoint in the variances, if `n` is the number of observations in the model. If `point` is greater than 1 it is interpreted to be the index of the breakpoint.
`fraction` | numerical. The number of central observations to be omitted. If `fraction` is smaller than 1, it is chosen to be `fraction*n` if `n` is the number of observations in the model.
`alternative` | a character string specifying the alternative hypothesis. The default is to test for increasing variances.
`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).
`data` | an optional data frame containing the variables in the model. By default the variables are taken from the environment which `gqtest` is called from.

### Details

The Goldfeld-Quandt test compares the variances of two submodels divided by a specified breakpoint and rejects if the variances differ.

Under H_0 the test statistic of the Goldfeld-Quandt test follows an F distribution with the degrees of freedom as given in `parameter`.

Examples can not only be found on this page, but also on the help pages of the data sets `bondyield`, `currencysubstitution`, `growthofmoney`, `moneydemand`, `unemployment`, `wages`.

### Value

A list with class `"htest"` containing the following components:

`statistic` | the value of the test statistic.
`parameter` | degrees of freedom.
`method` | a character string indicating what type of test was performed.
`alternative` | a character string describing the alternative hypothesis.
`p.value` | the p-value of the test.
`data.name` | a character string giving the name(s) of the data.

### References

S.M. Goldfeld & R.E. Quandt (1965), Some Tests for Homoskedasticity. Journal of the American Statistical Association 60, 539–547

W. Krämer & H. Sonnberger (1986), The Linear Regression Model under Test. Heidelberg: Physica

### See Also

`lm`

### Examples

    ## generate a regressor
    x <- rep(c(-1,1), 50)
    ## generate heteroskedastic and homoskedastic disturbances
    err1 <- c(rnorm(50, sd=1), rnorm(50, sd=2))
    err2 <- rnorm(100)
    ## generate a linear relationship
    y1 <- 1 + x + err1
    y2 <- 1 + x + err2
    ## perform Goldfeld-Quandt test
    gqtest(y1 ~ x)
    gqtest(y2 ~ x)

[Package lmtest version 0.9-37 Index]