A collection and description of functions for unit root testing. This is an interface to the unitroot tests implemented by B. Pfaff available through the R package urca which is required here.
Added functions based on the urca package include:
urdfTest | Augmented Dickey-Fuller test for unit roots, |
urersTest | Elliott-Rothenberg-Stock test for unit roots, |
urkpssTest | KPSS unit root test for stationarity, |
urppTest | Phillips-Perron test for unit roots, |
urspTest | Schmidt-Phillips test for unit roots, |
urzaTest | Zivot-Andrews test for unit roots. |
urdfTest(x, lags = 1, type = c("nc", "c", "ct"), doplot = TRUE)
urersTest(x, type = c("DF-GLS", "P-test"), model = c("constant", "trend"),
lag.max = 4, doplot = TRUE)
urkpssTest(x, type = c("mu", "tau"), lags = c("short", "long", "nil"),
use.lag = NULL, doplot = TRUE)
urppTest(x, type = c("Z-alpha", "Z-tau"), model = c("constant", "trend"),
lags = c("short", "long"), use.lag = NULL, doplot = TRUE)
urspTest(x, type = c("tau", "rho"), pol.deg = c(1, 2, 3, 4),
signif = c(0.01, 0.05, 0.1), doplot = TRUE)
urzaTest(x, model = c("intercept", "trend", "both"), lag, doplot = TRUE)
All tests return an object of class "fHTEST" with the
following slots:
the function call.
a data frame with the input data.
a character string giving the name of the data frame.
a list object which holds the output of the underlying test function.
a character string with the name of the test.
a character string with a brief description of the test.
The entries of the @test slot include the following components:
the value of the test statistic.
the lag order.
the p-value of the test.
a character string indicating what type of test was performed.
a character string giving the name of the data.
a character string describing the alternative hypothesis.
the name of the underlying function, which may be wrapped.
additional test results to be printed.
[ur*Test] -
a logical flag, by default TRUE. Should a diagnostical
plot be displayed?
[urersTest] -
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".
[urzaTest] -
the highest number of lagged endogenous differenced variables
to be included in the test regression.
[urkpssTest][urppTest] -
the maximum number of lags used for error term correction.
[urersTest] -
a character string dennoting the deterministic model used for
detrending, either "constant", the default, or
"trend".
[urppTest] -
a character string which determines the deterministic part in
the test regression, either "constant", the default, or
"trend".
[urzaTest] -
a character string specifying if the potential break occured
in either the "intercept", the linear "trend" or
in "both".
[urspTest] -
the polynomial degree in the test regression.
[urspTest] -
the significance level for the critical value of the test
statistic.
[urkpssTest] -
a character string which denotes the type of deterministic part,
either "mu", the default, or "tau".
[urppTest] -
a character string which specifies the test type, either
"Z-alpha", the default, or "Z-tau".
[urspTest] -
a character string which specifies the test type, either
"tau", the default, or "rho".
[urkpssTest] -
a character string specifying the number of lags. Allowed
arguments are lags=c("short", "long", "nil"), for more
information see the details section.
[urppTest] -
Use of a different lag number, specified by the user.
a numeric vector or time series object.
Bernhard Pfaff for the tests implemented in R's "urca" package,
Diethelm Wuertz for the Rmetrics R-port.
Unit Root Tests from Berhard Pfaff's "urca" Package:
Elliott-Rothenberg-Stock Test for Unit Roots:
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.
[urca:ur.ers]
KPSS Test for Unit Roots:
Performs the KPSS unit root test, where the Null hypothesis is
stationarity. The test types specify as deterministic component
either a constant "mu" or a constant with linear trend
"tau". lags="short" sets the number of lags to
root 4 of [4 times (n/100), whereas lags="long"
sets the number of lags to root 4 of [12 times (n/100)].
If lags="nil" is choosen, then no error correction is made.
Furthermore, one can specify a different number of maximum lags
by setting use.lag accordingly.
[urca:ur.kpss]
Phillips-Perron Test for Unit Roots:
Performs the Phillips and Perron unit root test. Beside the
Z statistics Z-alpha and Z-tau, the Z statistics for the
deterministic part of the test regression are computed, too.
For correction of the error term a Bartlett window is used.
[urca:ur.pp]
Schmidt-Phillips Test for Unit Roots:
Performs the Schmidt and Phillips unit root test, where under
the Null and Alternative Hypothesis the coefficients of the
deterministic variables are included. Two test types are available:
the "rho-test" and the "tau-test". Both tests are
extracted from the LM principle.
[urca:ur.sp]
Zivot-Andrews Test for Unit Roots:
Performs the Zivot and Andrews unit root test, which allows a
break at an unknown point in either the intercept, the linear
trend or in both. This test is based upon the recursive estimation
of a test regression. The test statistic is defined as the
minimum t-statistic of the coeffcient of the lagged endogenous
variable.
[urca:ur.za]
Banerjee A., Dolado J.J., Galbraith J.W., Hendry D.F. (1993); Cointegration, Error Correction, and the Econometric Analysis of Non-Stationary Data, Oxford University Press, Oxford.
Dickey, D.A., Fuller, W.A. (1979); Distribution of the estimators for autoregressive time series with a unit root, Journal of the American Statistical Association 74, 427--431.
Kwiatkowski D., Phillips P.C.B, Schmidt P., Shin Y. (1992); Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root, Journal of Econometrics 54, 159--178.
Perron P. (1988); Trends and Random Walks in Macroeconomic Time Series, Journal of Economic Dynamics and Control 12, 297--332.
Phillips P.C.B., Perron P. (1988); Testing for a unit root in time series regression, Biometrika 75, 335--346.
Said S.E., Dickey D.A. (1984); Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order, Biometrika 71, 599--607.
Schwert G.W. (1989); Tests for Unit Roots: A Monte Carlo Investigation, Journal of Business and Economic Statistics 2, 147--159.
## Time Series
# A time series which contains no unit-root:
x <- rnorm(1000)
# A time series which contains a unit-root:
y <- cumsum(c(0, x))
## ERS Test:
if(require("urca")) {
urersTest(x)
urersTest(y)
}
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