Elliott, Rothenberg and Stock Unit Root Test

Performs the Elliott, Rothenberg and Stock unit root test.

Usage

ur.ers(y, type = c("DF-GLS", "P-test"), model = c("constant", "trend"),
       lag.max = 4)

Arguments

y: Vector to be tested for a unit root.
type: Test type, either "DF-GLS" (default), or "P-test".
model: The deterministic model used for detrending.
lag.max: The maximum numbers of lags used for testing of a decent lag truncation for the "P-test" (BIC used), or the maximum number of lagged differences to be included in the test regression for "DF-GLS".

Details

To improve the power of the unit root test, Elliot, Rothenberg and Stock proposed a local to unity detrending of the time series. ERS developed a feasible point optimal test, "P-test", which takes serial correlation of the error term into account. The second test type is the "DF-GLS" test, which is an ADF-type test applied to the detrended data without intercept. Critical values for this test are taken from MacKinnon in case of model="constant" and else from Table 1 of Elliot, Rothenberg and Stock.

Value

An object of class ur.ers.

References

Elliott, G., Rothenberg, T.J. and Stock, J.H. (1996), Efficient Tests for an Autoregressive Unit Root, Econometrica, Vol. 64, No. 4, 813–836.

MacKinnon, J.G. (1991), Critical Values for Cointegration Tests, Long-Run Economic Relationships, eds. R.F. Engle and C.W.J. Granger, London, Oxford, 267–276.

Author

Bernhard Pfaff

Examples

data(nporg)
gnp <- na.omit(nporg[, "gnp.r"])
ers.gnp <- ur.ers(gnp, type="DF-GLS", model="const", lag.max=4)
summary(ers.gnp)
#> 
#> ############################################### 
#> # Elliot, Rothenberg and Stock Unit Root Test # 
#> ############################################### 
#> 
#> Test of type DF-GLS 
#> detrending of series with intercept 
#> 
#> 
#> Call:
#> lm(formula = dfgls.form, data = data.dfgls)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -39.767  -6.011   4.775  14.896  31.454 
#> 
#> Coefficients:
#>              Estimate Std. Error t value Pr(>|t|)   
#> yd.lag        0.02559    0.01793   1.427  0.15962   
#> yd.diff.lag1  0.45630    0.14668   3.111  0.00303 **
#> yd.diff.lag2  0.06223    0.15879   0.392  0.69672   
#> yd.diff.lag3 -0.02445    0.15965  -0.153  0.87886   
#> yd.diff.lag4 -0.10768    0.15110  -0.713  0.47925   
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 16.49 on 52 degrees of freedom
#> Multiple R-squared:  0.3825,	Adjusted R-squared:  0.3231 
#> F-statistic: 6.442 on 5 and 52 DF,  p-value: 9.956e-05
#> 
#> 
#> Value of test-statistic is: 1.4268 
#> 
#> Critical values of DF-GLS are:
#>                 1pct  5pct 10pct
#> critical values -2.6 -1.95 -1.62
#>