bgtest                package:lmtest                R Documentation

_B_r_e_u_s_c_h-_G_o_d_f_r_e_y _T_e_s_t

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

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

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

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

   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.

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

     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.

_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.

_A_u_t_h_o_r(_s):

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

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

     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.

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

     'dwtest'

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

          ## 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)

