gqtest            package:lmtest            R Documentation(latin1)

_G_o_l_d_f_e_l_d-_Q_u_a_n_d_t _T_e_s_t

_D_e_s_c_r_i_p_t_i_o_n:

     Goldfeld-Quandt test against heteroskedasticity.

_U_s_a_g_e:

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

_A_r_g_u_m_e_n_t_s:

 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.

_D_e_t_a_i_l_s:

     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'.

_V_a_l_u_e:

     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.

_R_e_f_e_r_e_n_c_e_s:

     S.M. Goldfeld & R.E. Quandt (1965), Some Tests for
     Homoskedasticity. _Journal of the American Statistical
     Association_ *60*, 539-547

     W. Krmer & H. Sonnberger (1986), _The Linear Regression Model
     under Test_. Heidelberg: Physica

_S_e_e _A_l_s_o:

     'lm'

_E_x_a_m_p_l_e_s:

     ## 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)

