dwtest                package:lmtest                R Documentation

_D_u_r_b_i_n-_W_a_t_s_o_n _T_e_s_t

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

     Performs the Durbin-Watson test for autocorrelation of
     disturbances.

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

     dwtest(formula, iterations = 15, exact = NULL, tol = 1e-10,
       data = list())

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

 formula: a symbolic describtion for the model to be tested.

iterations: an integer specifying the number of iterations when
          calculating the p-value with the "pan" algorithm.

   exact: logical. If set to `FALSE' a normal approximation will be
          used to compute the p value, if `TRUE' the "pan" algorithm is
          used. The default is to use "pan" if the sample size is <
          100.

     tol: tolerance. Eigenvalues computed have to be greater than `tol'
          to be treated as non-zero.

    data: an optional data frame containing the variables in the model.
          By default the variables are taken from the environment which
          `dwtest' is called from.

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

     The Durbin-Watson test has the null hypothesis "rho = 0", this
     implementation is built for the alternative "rho > 0". The null
     distribution of the Durbin-Watson test statistic is a linear
     combination of chi-squared distributions. The p value is computed
     using a Fortran version of the Applied Statistics Algorithm AS 153
     by Farebrother (1980, 1984). This algorithm is called "pan" or
     "gradsol". For large sample sizes the algorithm might fail to
     compute the p value; in that case a warning is printed and an
     approximate p value will be given; this p value is computed using
     a normal approximation with mean and variance of the Durbin-Watson
     test statistic.

     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:

     An object of class `"htest"' containing: 

statistic: the test statistic.

 p.value: the corresponding p-value.

  method: a character string with the method used.

data.name: a character string with the data name.

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

     J. Durbin & G.S. Watson (1950), Testing for Serial Correlation in
     Least Squares Regression I. Biometrika 37, 409-428

     J. Durbin & G.S. Watson (1951), Testing for Serial Correlation in
     Least Squares Regression II. Biometrika 38, 159-178

     J. Durbin & G.S. Watson (1971), Testing for Serial Correlation in
     Least Squares Regression III. Biometrika 58, 1-19

     R.W. Farebrother (1980), Pan's Procedure for the Tail
     Probabilities of the Durbin-Watson Statistic (Corr: 81V30 p189; AS
     R52: 84V33 p363- 366; AS R53: 84V33 p366- 369). Applied Statistics
     29,  224-227

     R. W. Farebrother (1984), [AS R53] A Remark on Algorithms AS 106
     (77V26 p92-98), AS 153 (80V29 p224-227) and AS 155: The
     Distribution of a Linear Combination of $\chi^2$ Random Variables
     (80V29 p323-333) Applied Statistics 33, 366-369

     W. Kraemer & 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 two AR(1) error terms with parameter
     ## rho = 0 (white noise) and rho = 0.9 respectively
     err1 <- rnorm(100)

     ## generate regressor and dependent variable
     x <- rep(c(-1,1), 50)
     y1 <- 1 + x + err1

     ## perform Durbin-Watson test
     dwtest(y1 ~ x)

     if(library(ts, logical = TRUE)) {
     err2 <- filter(err1, 0.9, method="recursive")
     y2 <- 1 + x + err2
     dwtest(y2 ~ x) }

