Augmented-Dickey-Fuller Unit Root Test

Performs the augmented Dickey-Fuller unit root test.

Usage

ur.df(y, type = c("none", "drift", "trend"), lags = 1,
      selectlags = c("Fixed", "AIC", "BIC"))

Arguments

y: Vector to be tested for a unit root.
type: Test type, either "none", "drift" or "trend".
lags: Number of lags for endogenous variable to be included.
selectlags: Lag selection can be achieved according to the Akaike "AIC" or the Bayes "BIC" information criteria. The maximum number of lags considered is set by lags. The default is to use a "fixed" lag length set by lags.

Details

The function ur.df() computes the augmented Dickey-Fuller test. If type is set to "none" neither an intercept nor a trend is included in the test regression. If it is set to "drift" an intercept is added and if it is set to "trend" both an intercept and a trend is added. The critical values are taken from Hamilton (1994) and Dickey and Fuller(1981).

Value

An object of class ur.df.

References

Dickey, D. A. and Fuller, W. A. (1979), Distributions of the Estimators For Autoregressive Time Series with a Unit Root, Journal of the American Statistical Association, 75, 427–431.

Dickey, D. A. and Fuller, W. A. (1981), Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root, Econometrica, 49, 1057–1072.

Hamilton (1994), Time Series Analysis, Princeton University Press.

Author

Bernhard Pfaff

Examples

data(Raotbl3)
attach(Raotbl3)
lc.df <- ur.df(y=lc, lags=3, type='trend')
summary(lc.df)
#> 
#> ############################################### 
#> # Augmented Dickey-Fuller Test Unit Root Test # 
#> ############################################### 
#> 
#> Test regression trend 
#> 
#> 
#> Call:
#> lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
#> 
#> Residuals:
#>       Min        1Q    Median        3Q       Max 
#> -0.044714 -0.006525  0.000129  0.006225  0.045353 
#> 
#> Coefficients:
#>               Estimate Std. Error t value Pr(>|t|)   
#> (Intercept)  0.7976591  0.3547775   2.248   0.0270 * 
#> z.lag.1     -0.0758706  0.0338880  -2.239   0.0277 * 
#> tt           0.0004915  0.0002159   2.277   0.0252 * 
#> z.diff.lag1 -0.1063957  0.1006744  -1.057   0.2934   
#> z.diff.lag2  0.2011373  0.1012373   1.987   0.0500 . 
#> z.diff.lag3  0.2998586  0.1020548   2.938   0.0042 **
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.01307 on 89 degrees of freedom
#> Multiple R-squared:  0.1472,	Adjusted R-squared:  0.09924 
#> F-statistic: 3.071 on 5 and 89 DF,  p-value: 0.01325
#> 
#> 
#> Value of test-statistic is: -2.2389 3.7382 2.5972 
#> 
#> Critical values for test statistics: 
#>       1pct  5pct 10pct
#> tau3 -4.04 -3.45 -3.15
#> phi2  6.50  4.88  4.16
#> phi3  8.73  6.49  5.47
#>