UnitrootUrcaInterface: Unit Root Time Series Tests

In fUnitRoots: Rmetrics - Modelling Trends and Unit Roots

Unit Root Time Series Tests

Description

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.

Usage

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)

Arguments

doplot	[ur*Test] - a logical flag, by default TRUE. Should a diagnostical plot be displayed?
lag.max	[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".
lag	[urzaTest] - the highest number of lagged endogenous differenced variables to be included in the test regression.
lags	[urkpssTest][urppTest] - the maximum number of lags used for error term correction.
model	[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".
pol.deg	[urspTest] - the polynomial degree in the test regression.
signif	[urspTest] - the significance level for the critical value of the test statistic.

type	[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".
use.lag	[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.
x	a numeric vector or time series object.

Details

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]

Value

All tests return an object of class "fHTEST" with the following slots:

@call	the function call.
@data	a data frame with the input data.
@data.name	a character string giving the name of the data frame.
@test	a list object which holds the output of the underlying test function.
@title	a character string with the name of the test.
@description	a character string with a brief description of the test.

The entries of the @test slot include 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.
$name	the name of the underlying function, which may be wrapped.
$output	additional test results to be printed.

Note

The functions ur*Test() fullfill the naming conventions of Rmetrics, return an S4 object named fHTEST as any other hypothesis test from Rmetrics, and allow for timeSeries objects as input. These are the only differences to the original implementation of the functions.

Fur further details we refer to the manual pages of the urca package which is required for all these.

Author(s)

Bernhard Pfaff for the tests implemented in R's "urca" package,
Diethelm Wuertz for the Rmetrics R-port.

References

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.

Examples

## 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)
  }

fUnitRoots documentation built on Sept. 9, 2022, 3:06 p.m.