Title:	Rmetrics - Modelling Trends and Unit Roots
Version:	4052.82
Description:	Provides four addons for analyzing trends and unit roots in financial time series: (i) functions for the density and probability of the augmented Dickey-Fuller Test, (ii) functions for the density and probability of MacKinnon's unit root test statistics, (iii) reimplementations for the ADF and MacKinnon Test, and (iv) an 'urca' Unit Root Test Interface for Pfaff's unit root test suite.
Depends:	R (≥ 2.15.1)
Imports:	timeSeries, fBasics, urca, graphics, methods, stats, utils
Suggests:	RUnit, interp
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
URL:	https://geobosh.github.io/fUnitRootsDoc/ (doc), https://CRAN.R-project.org/package=fUnitRoots, https://www.rmetrics.org
BugReports:	https://r-forge.r-project.org/tracker/?atid=633&group_id=156&func=browse
NeedsCompilation:	yes
Packaged:	2025-12-19 11:27:34 UTC; georgi
Author:	Diethelm Wuertz [aut] (original code), Tobias Setz [aut], Yohan Chalabi [aut], Georgi N. Boshnakov [cre]
Maintainer:	Georgi N. Boshnakov <georgi.boshnakov@manchester.ac.uk>
Repository:	CRAN
Date/Publication:	2025-12-19 13:50:14 UTC

Modelling Trends and Unit Roots

Description

The Rmetrics "fUnitRoots" package is a collection of functions to model trends and to analyze unit roots.

1 Introduction

The 'fUnitroots' provides four addons for analyzing trends and unit roots in financial time series: (i) functions for the density and probability of the augmented Dickey-Fuller Test, (ii) functions for the density and probability of MacKinnon's unit root test statistics, (iii) reimplementations for the ADF and MacKinnon Test, and (iv) an 'urca' Unit Root Test Interface for Pfaff's unit root test suite.

2 Dickey-Fuller p Values

The section provides functions to compute the distribution and quantile functions for the ADF unit root test statistics.

    padf            returns the cumulative probability for the ADF test
    qadf            returns the quantiles for the ADF test
    adfTable        tables p values for ADF test
    

3 Mc Kinnon p Values

The section provides functions to compute the distribution and quantile functions for MacKinnon's unit root test statistics.

    punitroot       returns the cumulative probability
    qunitroot       returns the quantiles of the unit root test statistics
    unitrootTable   tables p values from MacKinnon's response surface
    

4 Unit Root Time Series Tests

This section provides two functions for unit root testing of financial time series, the ADF tests based on Banerjee's et al. tables and the unit root tests based on J.G. McKinnons' tables:

    adfTest         augmented Dickey-Fuller test for unit roots
    unitrootTest    the same based on McKinnons's test statistics
    

5 "urca"" Unit Root Test Interface

This is an interface to the unitroot tests suite implemented by Bernhard Pfaff available through the R package "urca"

    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
    

About Rmetrics

The fUnitroots Rmetrics package is written for educational support in teaching "Computational Finance and Financial Engineering" and licensed under the GPL.

Dickey-Fuller p Values

Description

A collection and description of functions to compute the distribution and quantile function for the ADF unit root test statistics.

Usage

padf(q, N = Inf, trend = c("nc", "c", "ct"), statistic = c("t", "n")) 
qadf(p, N = Inf, trend = c("nc", "c", "ct"), statistic = c("t", "n"))

adfTable(trend = c("nc", "c", "ct"), statistic = c("t", "n"), 
    includeInf = TRUE)

Arguments

Details

padf computes cumulative probabilities for the ADF test.

qadf computes quantiles for the ADF test.

With sufficiently fine grid for the first argument, padf and qadf compute, respectively, cumulative distribution functions and quantile functions of ADF test statistics.

adfTable produces tables of p-values for ADF tests.

Value

for padf and qadf, a named numeric vector with attribute "control" holding N,

for adfTable, an object from class "gridData", which is a list with the following components:

The "gridData" object contains also attribute "control" with information about the requested test.

Note

padf and qadf is based on the tables from A. Banerjee et al. (1993). Interpolation is used For value of N not in the tables. For small N (N < 25) the result is NA.

Author(s)

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.

Examples

padf(q = -2:2, N = 25)
qadf(p = (1:9)/10, N = 25)
adfTable()

MacKinnon's Unit Root p Values

Description

A collection and description of functions to compute the distribution and quantile function for MacKinnon's unit root test statistics.

Usage

punitroot(q, N = Inf, trend = c("c", "nc", "ct", "ctt"), 
    statistic = c("t", "n"), na.rm = FALSE)
qunitroot(p, N = Inf, trend = c("c", "nc", "ct", "ctt"), 
    statistic = c("t", "n"), na.rm = FALSE)
    
unitrootTable(trend = c("c", "nc", "ct", "ctt"), statistic = c("t", "n")) 

Arguments

Details

punitroot computes the cumulative probability of the asymptotic or finite sample distribution of the unit root test statistics.

qunitroot computes the quantiles of the asymptotic or finite sample distribution of the unit root test statistics, given the probabilities.

unitrootTable produces tables of p-values from MacKinnon's response surface.

Value

for punitroot and qunitroot, a numeric vector,

for unitrootTable, a matrix with attribute "control" containing information about the type of test.

Note

The function punitroot and qunitroot use Fortran routines and the response surface approach from J.G. MacKinnon (1988). Many thanks to J.G. MacKinnon putting his code and tables under the GPL license, which made this implementation possible.

Author(s)

J.G. MacKinnon for the underlying Fortran routine and the tables,
Diethelm Wuertz for the Rmetrics R-port.

References

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.

MacKinnon, J.G. (1996); Numerical distribution functions for unit root and cointegration tests, Journal of Applied Econometrics 11, 601–618.

Phillips, P.C.B., Perron, P. (1988); Testing for a unit root in time series regression, Biometrika 75, 335–346.

Examples

 
## Asymptotic quantile of t-statistic
qunitroot(0.95, trend = "nc", statistic = "t")
## 1st argument a vector
qunitroot(c(0.90, 0.95), trend = "nc", statistic = "t")

## Finite sample quantile of n-statistic
qunitroot(0.95, N = 100, trend = "nc", statistic = "n") 


## Asymptotic cumulative probability of t-statistic
punitroot(1.2836, trend = "nc", statistic = "t")

## Finite sample cumulative probability of n-statistic
punitroot(1.2836, N = 100, trend = "nc", statistic = "n")

   
## Mac Kinnon's unitrootTable
unitrootTable(trend = "nc")

Unit root time series tests

Description

Carry out augmented Dickey-Fuller tests for unit roots based on Banerjee's et al. tables and on J.G. McKinnons' numerical distribution functions.

Usage

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)

Arguments

Details

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.

unitrootTest() computes test statistics and p-values using McKinnon's response surface approach.

Value

an object from S4 class "fHTEST" with the following slots:

The entries of the @test slot include the following components:

Author(s)

Adrian Trapletti for the tests adapted from R's "tseries" 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.

MacKinnon, J.G. (1996); Numerical distribution functions for unit root and cointegration tests, Journal of Applied Econometrics 11, 601–618.

Said S.E., Dickey D.A. (1984); Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order, Biometrika 71, 599–607.

Examples

## a time series which contains no unit-root:
x <- rnorm(1000)  
## a time series which contains a unit-root:
y <- cumsum(c(0, x))
   
adfTest(x)
adfTest(y)
   
unitrootTest(x)
unitrootTest(y)     

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:

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

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:

The entries of the @test slot include the following components:

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

## 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)
}