| dwtest {lmtest} | R Documentation |
Performs the Durbin-Watson test for autocorrelation of disturbances.
dwtest(formula, iterations = 15, exact = NULL, tol = 1e-10, data = list())
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. |
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.
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. |
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
## 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) }