tseries (version 0.10-24)

adf.test: Augmented Dickey--Fuller Test

Description

Computes the Augmented Dickey-Fuller test for the null that x has a unit root.

Usage

adf.test(x, alternative = c("stationary", "explosive"),
         k = trunc((length(x)-1)^(1/3)))

Arguments

x

a numeric vector or time series.

alternative

indicates the alternative hypothesis and must be one of "stationary" (default) or "explosive". You can specify just the initial letter.

k

the lag order to calculate the test statistic.

Value

• A list with class "htest" containing the following components:
• statistic
  the value of the test statistic.
• parameter
  the lag order.
• p.value
  the p-value of the test.
• method
  a character string indicating what type of test was performed.
• data.name
  a character string giving the name of the data.
• alternative
  a character string describing the alternative hypothesis.

Details

The general regression equation which incorporates a constant and a linear trend is used and the t-statistic for a first order autoregressive coefficient equals one is computed. The number of lags used in the regression is k. The default value of trunc((length(x)-1)^(1/3)) corresponds to the suggested upper bound on the rate at which the number of lags, k, should be made to grow with the sample size for the general ARMA(p,q) setup. Note that for k equals zero the standard Dickey-Fuller test is computed. The p-values are interpolated from Table 4.2, p. 103 of Banerjee et al. (1993). If the computed statistic is outside the table of critical values, then a warning message is generated. Missing values are not allowed.

References

A. Banerjee, J. J. Dolado, J. W. Galbraith, and D. F. Hendry (1993): Cointegration, Error Correction, and the Econometric Analysis of Non-Stationary Data, Oxford University Press, Oxford. S. E. Said and D. A. Dickey (1984): Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order. Biometrika 71, 599--607.

See Also

pp.test

Examples

x <- rnorm(1000)  # no unit-root
adf.test(x)

y <- diffinv(x)   # contains a unit-root
adf.test(y)