UnitrootTests {fSeries} | R Documentation |
A collection and description of functions
for unit root testing. The family of tests
includes ADF tests based on Banerjee's et al.
tables and on J.G. McKinnons' numerical
distribution functions. In addition we have
included tests written by B. Pfaff.
The functions are:
adfTest | Augmented Dickey–Fuller test for unit roots, |
unitrootTest | the same based on McKinnons's test statistics. |
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. |
Note, that the contributed R package urca
is required!
urTest(x, method = c("unitroot", "adf", "urers", "urkpss", "urpp", "ursp", "urza"), title = NULL, description = NULL, ...) unitrootTest(x, lags = 1, type = c("nc", "c", "ct"), title = NULL, description = NULL) adfTest(x, lags = 1, type = c("nc", "c", "ct"), title = NULL, description = NULL) 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)
description |
a character string which allows for a brief description. |
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. |
method |
[urTest] - a character string describing the desired method, one of: "unitroot" , "adf" , "urers" , "urkpss" ,
"urpp" , "ursp" , or "urza" .
|
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. |
title |
a character string which allows for a project title. |
type |
[adfTest][unitrootTest] - a character string describing the type of the unit root regression. Valid choices are "nc" for a regression
with no intercept (constant) nor time trend, and "c"
for a regression with an intercept (constant) but no time
trend, "ct" for a regression with an intercept
(constant) and a time trend. The default is "c" .
[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. |
... |
[urTest] - optional arguments passed to the underlying test functions. |
ADF Tests:
The adftest
computes test statistics and p values along
the implementation from Trapletti's augmented Dickey–Fuller test
for unit roots. In contrast to Trapletti's function three kind
of test types can be selected.
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]
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. |
$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. |
The ur*Test
wrapper functions 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. The Rmetrics wrappers
were tested with urca
version 0.7.9.
If you are running Rmetrics under an operating system where the
R-package urca
or one of the other packages from the
dependency tree is not available you can load the required
functions through the command xmpfSeries() and select
funUrca from the menu. A minimalist copy of "urca"
and required dependent functions are saved in the demo
file funUrca.R
.
Fur further details we refer to the manual pages of the
"urca"
package.
Adrian Trapletti for the tests adapted from R's "tseries" package,
Bernhard Pfaff for the tests wrapped from R's "urca" package,
Diethelm Wuertz for the Rmetrics R-port.
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.
MacKinnon, J.G. (1996); Numerical distribution functions for unit root and cointegration tests, Journal of Applied Econometrics 11, 601–618.
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.
## SOURCE("fSeries.2B-UnitrootTests") ## adfTest - # A time series which contains no unit-root: x = rnorm(1000) # A time series which contains a unit-root: y = cumsum(c(0, x)) # Test: adfTest(x) adfTest(y) ## unitrootTest - unitrootTest(x) unitrootTest(y) ## ur*Test - # Unit Root Tests build on Bernhard Pfaff's Implementation: # Examples can be found in the demo file "xmpTestUnitRoots".