MANUAL

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Package ‘CPAT’
October 15, 2018
Title Change Point Analysis Tests
Version 0.1.0
Description Implements several statistical tests for structural change in R.
Depends R (>= 3.2)
Suggests cointReg (>= 0.2), foreach (>= 1.4), doParallel (>= 1.0),
ggplot2 (>= 2.2), dplyr (>= 0.7), tikzDevice (>= 0.12),
testthat (>= 2.0)
Imports stats (>= 3.2), utils (>= 3.2), grDevices (>= 3.2), Rdpack (>=
0.9), methods (>= 3.2), Rcpp (>= 0.12), purrr (>= 0.2)
RdMacros Rdpack
SystemRequirements GNU make
License MIT + file LICENSE
Encoding UTF-8
LazyData true
LinkingTo Rcpp, RcppArmadillo
RoxygenNote 6.1.0
NeedsCompilation yes
Author Curtis Miller [aut, cre]
Maintainer Curtis Miller <cmiller@math.utah.edu>
Rtopics documented:
.onAttach .......................................... 2
Andrews.test ........................................ 3
andrews_test......................................... 3
andrews_test_reg ...................................... 4
banks ............................................ 5
CPAT_startup_message................................... 5
cpt_consistent_var ..................................... 6
CUSUM.test......................................... 6
DE.test ........................................... 7
dZn ............................................. 8
ff............................................... 9
getLongRunWeights .................................... 10
get_lrv_vec ......................................... 10
1
2.onAttach
HR.test ........................................... 11
HS.test............................................ 12
pdarling_erdos ....................................... 13
phidalgo_seo ........................................ 13
pkolmogorov ........................................ 14
pZn ............................................. 14
qdarling_erdos ....................................... 15
qhidalgo_seo ........................................ 15
qkolmogorov ........................................ 16
qZn ............................................. 16
rchangepoint ........................................ 17
sim_de_stat ......................................... 18
sim_hs_stat ......................................... 19
sim_Vn ........................................... 20
sim_Vn_stat......................................... 21
sim_Zn ........................................... 22
sim_Zn_stat......................................... 23
stat_de............................................ 24
stat_hs............................................ 25
stat_Vn ........................................... 27
stat_Zn ........................................... 28
%s%............................................. 30
%s0% ............................................ 30
Index 31
.onAttach Package Attach Hook Function
Description
Hook triggered when package attached
Usage
.onAttach(lib, pkg)
Arguments
lib a character string giving the library directory where the package defining the
namespace was found
pkg a character string giving the name of the package
Examples
CPAT:::.onAttach(.libPaths()[1], "CPAT")
Andrews.test 3
Andrews.test Andrews’ Test for End-of-Sample Structural Change
Description
Performs Andrews’ test for end-of-sample structural change, as described in (Andrews 2003). This
function works for both univariate and multivariate data depending on the nature of xand whether
formula is specified. This function is thus an interface to andrews_test and andrews_test_reg;
see the documentation of those functions for more details.
Usage
Andrews.test(x, M, formula = NULL)
Arguments
xData to test for change in mean (either a vector or data.frame)
MNumeric index of the location of the first potential change point
formula The regression formula, which will be passed to lm
Value
Ahtest-class object containing the results of the test
References
Andrews DWK (2003). “End-of-Sample Instability Tests.” Econometrica,71(6), 1661–1694. ISSN
00129682, 14680262, https://www.jstor.org/stable/1555535.
Examples
Andrews.test(rnorm(1000), M = 900)
x <- rnorm(1000)
y <- 1 + 2 * x + rnorm(1000)
df <- data.frame(x, y)
Andrews.test(df, y ~ x, M = 900)
andrews_test Univariate Andrews Test for End-of-Sample Structural Change
Description
This implements Andrews’ test for end-of-sample change, as described by Andrews (2003). This
test was derived for detecting a change in univariate data. See (Andrews 2003) for a description of
the test.
Usage
andrews_test(x, M, pval = TRUE, stat = TRUE)
4andrews_test_reg
Arguments
xVector of the data to test
MNumeric index of the location of the first potential change point
pval If TRUE, return a p-value
stat If TRUE, return a test statistic
Value
If both pval and stat are TRUE, a list containing both; otherwise, a number for one or the other,
depending on which is TRUE
References
Andrews DWK (2003). “End-of-Sample Instability Tests.” Econometrica,71(6), 1661–1694. ISSN
00129682, 14680262, https://www.jstor.org/stable/1555535.
Examples
CPAT:::andrews_test(rnorm(1000), M = 900)
andrews_test_reg Multivariate Andrews’ Test for End-of-Sample Structural Change
Description
This implements Andrews’ test for end-of-sample change, as described by Andrews (2003). This
test was derived for detecting a change in multivarate data, aso originally described. See (Andrews
2003) for a description of the test.
Usage
andrews_test_reg(formula, data, M, pval = TRUE, stat = TRUE)
Arguments
formula The regression formula, which will be passed to lm
data data.frame containing the data
MNumeric index of the location of the first potential change point
pval If TRUE, return a p-value
stat If TRUE, return a test statistic
Value
If both pval and stat are TRUE, a list containing both; otherwise, a number for one or the other,
depending on which is TRUE
References
Andrews DWK (2003). “End-of-Sample Instability Tests.” Econometrica,71(6), 1661–1694. ISSN
00129682, 14680262, https://www.jstor.org/stable/1555535.
banks 5
Examples
x <- rnorm(1000)
y <- 1 + 2 * x + rnorm(1000)
df <- data.frame(x, y)
CPAT:::andrews_test_reg(y ~ x, data = df, M = 900)
banks Bank Portfolio Returns
Description
Data set representing the returns of an industry portfolio representing the banking industry based on
company four-digit SIC codes, obtained from the data library maintained by Kenneth French. Data
ranges from July 1, 1926 to October 31, 2017.
Usage
banks
Format
A data frame with 24099 rows and 1 variable:
Banks The return of a portfolio representing the banking industry
Row names are dates in YYYY-MM-DD format.
Source
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
CPAT_startup_message Create Package Startup Message
Description
Makes package startup message.
Usage
CPAT_startup_message()
Examples
CPAT:::CPAT_startup_message()
6CUSUM.test
cpt_consistent_var Variance Estimation Consistent Under Change
Description
Estimate the variance (using the sum of squared errors) with an estimator that is consistent when
the mean changes at a known point.
Usage
cpt_consistent_var(x, k)
Arguments
xA numeric vector for the data set
kThe potential change point at which the data set is split
Details
This is the estimator
ˆσ2
T,t =T−1 t
X
s=1 Xs−¯
Xt2+
T
X
s=t+1 Xs−˜
XT−t2!
where ¯
Xt=t−1Pt
s=1 Xsand ˜
XT−t= (T−t)−1PT
s=t+1 Xs. In this implementation, Tis
computed automatically as length(x) and kcorresponds to t, a potential change point.
Value
The estimated change-consistent variance
Examples
CPAT:::cpt_consistent_var(c(rnorm(500, mean = 0), rnorm(500, mean = 1)), k = 500)
CUSUM.test CUSUM Test
Description
Performs the (univariate) CUSUM test for change in mean, as described in (Rice et al. ). This
is effectively an interface to stat_Vn; see its documentation for more details. p-values are com-
puted using pkolmogorov, which represents the limiting distribution of the statistic under the null
hypothesis.
Usage
CUSUM.test(x, use_kernel_var = FALSE, stat_plot = FALSE,
kernel = "ba", bandwidth = "and")
DE.test 7
Arguments
xData to test for change in mean
use_kernel_var Set to TRUE to use kernel methods for long-run variance estimation (typically
used when the data is believed to be correlated); if FALSE, then the long-run vari-
ance is estimated using ˆσ2
T,t =T−1Pt
s=1 Xs−¯
Xt2+PT
s=t+1 Xs−˜
XT−t2,
where ¯
Xt=t−1Pt
s=1 Xsand ˜
XT−t= (T−t)−1PT
s=t+1 Xs
stat_plot Whether to create a plot of the values of the statistic at all potential change points
kernel If character, the identifier of the kernel function as used in cointReg (see getLongRunVar);
if function, the kernel function to be used for long-run variance estimation (de-
fault is the Bartlett kernel in cointReg)
bandwidth If character, the identifier for how to compute the bandwidth as defined in coin-
tReg (see getBandwidth); if function, a function to use for computing the band-
width; if numeric, the bandwidth value to use (the default is to use Andrews’
method, as used in cointReg)
Value
Ahtest-class object containing the results of the test
References
Rice G, Miller C, Horváth L (????). “A new class of change point test of Rényi type.” in-press.
Examples
CUSUM.test(rnorm(1000))
CUSUM.test(rnorm(1000), use_kernel_var = TRUE, kernel = "bo",
bandwidth = "nw")
DE.test Darling-Erdös Test
Description
Performs the (univariate) Darling-Erdös test for change in mean, as described in (Rice et al. ). This
is effectively an interface to stat_de; see its documentation for more details. p-values are computed
using pdarling_erdos, which represents the limiting distribution of the test statistic under the null
hypothesis when aand bare chosen appropriately. (Change those parameters at your own risk!)
Usage
DE.test(x, a = log, b = log, use_kernel_var = FALSE,
stat_plot = FALSE, kernel = "ba", bandwidth = "and")
8dZn
Arguments
xData to test for change in mean
aThe function that will be composed with l(x) = (2 log x)1/2
bThe function that will be composed with u(x) = 2 log x+1
2log log x−1
2log π
use_kernel_var Set to TRUE to use kernel methods for long-run variance estimation (typically
used when the data is believed to be correlated); if FALSE, then the long-run vari-
ance is estimated using ˆσ2
T,t =T−1Pt
s=1 Xs−¯
Xt2+PT
s=t+1 Xs−˜
XT−t2,
where ¯
Xt=t−1Pt
s=1 Xsand ˜
XT−t= (T−t)−1PT
s=t+1 Xs
stat_plot Whether to create a plot of the values of the statistic at all potential change points
kernel If character, the identifier of the kernel function as used in cointReg (see getLongRunVar);
if function, the kernel function to be used for long-run variance estimation (de-
fault is the Bartlett kernel in cointReg)
bandwidth If character, the identifier for how to compute the bandwidth as defined in coin-
tReg (see getBandwidth); if function, a function to use for computing the band-
width; if numeric, the bandwidth value to use (the default is to use Andrews’
method, as used in cointReg)
Value
Ahtest-class object containing the results of the test
References
Rice G, Miller C, Horváth L (????). “A new class of change point test of Rényi type.” in-press.
Examples
DE.test(rnorm(1000))
DE.test(rnorm(1000), use_kernel_var = TRUE, kernel = "bo", bandwidth = "nw")
dZn Rényi-Type Statistic Limiting Distribution Density Function
Description
Function for computing the value of the density function of the limiting distribution of the Rényi-
type statistic.
Usage
dZn(x, summands = NULL)
Arguments
xPoint at which to evaluate the density function (note that this parameter is not
vectorized)
summands Number of summands to use in summation (the default should be machine ac-
curate)
ff 9
Value
Value of the density function at x
Examples
CPAT:::dZn(1)
ff Fama-French Five Factors
Description
Data set containing the five factors described by Fama and French (2015), from the data library
maintained by Kenneth French. Data ranges from July 1, 1963 to October 31, 2017.
Usage
ff
Format
A data frame with 13679 rows and 6 variables:
Mkt.RF Market excess returns
RF The risk-free rate of return
SMB The return on a diversified portfolio of small stocks minus return on a diversified portfolio of
big stocks
HML The return of a portfolio of stocks with a high book-to-market (B/M) ratio minus the return
of a portfolio of stocks with a low B/M ratio
RMW The return of a portfolio of stocks with robust profitability minus a portfolio of stocks with
weak profitability
CMA The return of a portfolio of stocks with conservative investment minus the return of a port-
folio of stocks with aggressive investment
Row names are dates in YYYYMMDD format.
Source
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
10 get_lrv_vec
getLongRunWeights Weights for Long-Run Variance
Description
Compute some weights for long-run variance. This code comes directly from the source code of
cointReg; see getLongRunWeights.
Usage
getLongRunWeights(n, bandwidth, kernel = "ba")
Arguments
nLength of weights’ vector
bandwidth A number for the bandwidth
kernel The kernel function; see getLongRunVar for possible values
Value
List with components wcontaining the vector of weights and upper, the index of the largest non-
zero entry in w
Examples
CPAT:::getLongRunWeights(10, 1)
get_lrv_vec Long-Run Variance Estimation With Possible Change Points
Description
Computes the estimates of the long-run variance in a change point context, as described in (Rice et
al. ). By default it uses kernel and bandwidth selection as used in the package cointReg, though
changing the parameters kernel and bandwidth can change this behavior. If cointReg is not in-
stalled, the Bartlett internal (defined internally) will be used and the bandwidth will be the square
root of the sample size.
Usage
get_lrv_vec(dat, kernel = "ba", bandwidth = "and")
Arguments
dat The data vector
kernel If character, the identifier of the kernel function as used in cointReg (see getLongRunVar);
if function, the kernel function to be used for long-run variance estimation (de-
fault is the Bartlett kernel in cointReg)
bandwidth If character, the identifier for how to compute the bandwidth as defined in coin-
tReg (see getBandwidth); if function, a function to use for computing the band-
width; if numeric, the bandwidth value to use (the default is to use Andrews’
method, as used in cointReg)
HR.test 11
Value
A vector of estimates of the long-run variance
References
Rice G, Miller C, Horváth L (????). “A new class of change point test of Rényi type.” in-press.
Examples
x <- rnorm(1000)
CPAT:::get_lrv_vec(x)
CPAT:::get_lrv_vec(x, kernel = "pa", bandwidth = "nw")
HR.test Rényi-Type Test
Description
Performs the (univariate) Rényi-type test for change in mean, as described in (Rice et al. ). This is
effectively an interface to stat_Zn; see its documentation for more details. p-values are computed
using pZn, which represents the limiting distribution of the test statistic under the null hypothesis,
which represents the limiting distribution of the test statistic under the null hypothesis when kn
represents a sequence tTsatisfying tT→ ∞ and tT/T →0as T→ ∞. (log and sqrt should be
good choices.)
Usage
HR.test(x, kn = log, use_kernel_var = FALSE, stat_plot = FALSE,
kernel = "ba", bandwidth = "and")
Arguments
xData to test for change in mean
kn A function corresponding to the trimming parameter tT; by default, the square
root function
use_kernel_var Set to TRUE to use kernel methods for long-run variance estimation (typically
used when the data is believed to be correlated); if FALSE, then the long-run vari-
ance is estimated using ˆσ2
T,t =T−1Pt
s=1 Xs−¯
Xt2+PT
s=t+1 Xs−˜
XT−t2,
where ¯
Xt=t−1Pt
s=1 Xsand ˜
XT−t= (T−t)−1PT
s=t+1 Xs; if custom_var
is not NULL, this argument is ignored
stat_plot Whether to create a plot of the values of the statistic at all potential change points
kernel If character, the identifier of the kernel function as used in cointReg (see getLongRunVar);
if function, the kernel function to be used for long-run variance estimation (de-
fault is the Bartlett kernel in cointReg)
bandwidth If character, the identifier for how to compute the bandwidth as defined in coin-
tReg (see getBandwidth); if function, a function to use for computing the band-
width; if numeric, the bandwidth value to use (the default is to use Andrews’
method, as used in cointReg)
12 HS.test
Value
Ahtest-class object containing the results of the test
References
Rice G, Miller C, Horváth L (????). “A new class of change point test of Rényi type.” in-press.
Examples
HR.test(rnorm(1000))
HR.test(rnorm(1000), use_kernel_var = TRUE, kernel = "bo", bandwidth = "nw")
HS.test Hidalgo-Seo Test
Description
Performs the (univariate) Hidalgo-Seo test for change in mean, as described in (Rice et al. ). This is
effectively an interface to stat_hs; see its documentation for more details. p-values are computed
using phidalgo_seo, which represents the limiting distribution of the test statistic when the null
hypothesis is true.
Usage
HS.test(x, corr = TRUE, stat_plot = FALSE)
Arguments
xData to test for change in mean
corr If TRUE, the long-run variance will be computed under the assumption of corre-
lated residuals; ignored if custom_var is not NULL or use_kernel_var is TRUE
stat_plot Whether to create a plot of the values of the statistic at all potential change points
Value
Ahtest-class object containing the results of the test
References
Rice G, Miller C, Horváth L (????). “A new class of change point test of Rényi type.” in-press.
Examples
HS.test(rnorm(1000))
HS.test(rnorm(1000), corr = FALSE)
pdarling_erdos 13
pdarling_erdos Darling-Erdös Statistic CDF
Description
CDF for the limiting distribution of the Darling-Erdös statistic.
Usage
pdarling_erdos(q)
Arguments
qQuantile input to CDF
Value
If Zis the random variable with this distribution, the quantity P(Z≤q)
Examples
CPAT:::pdarling_erdos(0.1)
phidalgo_seo Hidalgo-Seo Statistic CDF
Description
CDF of the limiting distribution of the Hidalgo-Seo statistic
Usage
phidalgo_seo(q)
Arguments
qQuantile input to CDF
Value
If Zis the random variable following the limiting distribution, the quantity P(Z≤q)
Examples
CPAT:::phidalgo_seo(0.1)
14 pZn
pkolmogorov Kolmogorov CDF
Description
CDF of the Kolmogorov distribution.
Usage
pkolmogorov(q, summands = ceiling(q * sqrt(72) + 3/2))
Arguments
qQuantile input to CDF
summands Number of summands for infinite sum (the default should have machine accu-
racy)
Value
If Zis the random variable following the Kolmogorov distribution, the quantity P(Z≤q)
Examples
CPAT:::pkolmogorov(0.1)
pZn Rènyi-Type Statistic CDF
Description
CDF for the limiting distribution of the Rènyi-type statistic.
Usage
pZn(q, summands = NULL)
Arguments
qQuantile input to CDF
summands Number of summands for infinite sum; if NULL, automatically determined
Value
If Zis the random variable following the limiting distribution, the quantity P(Z≤q)
Examples
CPAT:::pZn(0.1)
qdarling_erdos 15
qdarling_erdos Darling-Erdös Statistic Limiting Distribution Quantile Function
Description
Quantile function for the limiting distribution of the Darling-Erdös statistic.
Usage
qdarling_erdos(p)
Arguments
pThe probability associated with the desired quantile
Value
The quantile associated with p
Examples
CPAT:::qdarling_erdos(0.5)
qhidalgo_seo Hidalgo-Seo Statistic Limiting Distribution Quantile Function
Description
Quantile function for the limiting distribution of the Hidalgo-Seo statistic
Usage
qhidalgo_seo(p)
Arguments
pThe probability associated with the desired quantile
Value
A The quantile associated with p
Examples
CPAT:::qhidalgo_seo(0.5)
16 qZn
qkolmogorov Kolmogorov Distribution Quantile Function
Description
Quantile function for the Kolmogorov distribution.
Usage
qkolmogorov(p, summands = 500, interval = c(0, 100),
tol = .Machine$double.eps, ...)
Arguments
pValue of the CDF at the quantile
summands Number of summands for infinite sum
interval, tol, ...
Arguments to be passed to uniroot
Details
This function uses uniroot for finding this quantity, and many of the the accepted parameters are
arguments for that function; see its documentation for more details.
Value
The quantile associated with p
Examples
CPAT:::qkolmogorov(0.5)
qZn Rènyi-Type Statistic Quantile Function
Description
Quantile function for the limiting distribution of the Rènyi-type statistic.
Usage
qZn(p, summands = 500, interval = c(0, 100),
tol = .Machine$double.eps, ...)
Arguments
pValue of the CDF at the quantile
summands Number of summands for infinite sum
interval, tol, ...
Arguments to be passed to uniroot
rchangepoint 17
Details
This function uses uniroot for finding this quantity, and many of the the accepted parameters are
arguments for that function; see its documentation for more details.
Value
The quantile associated with p
Examples
CPAT:::qZn(0.5)
rchangepoint Simulate Univariate Data With a Single Change Point
Description
This function simulates univariate data with a structural change.
Usage
rchangepoint(n, changepoint = NULL, mean1 = 0, mean2 = 0,
dist = rnorm, meanparam = "mean", ...)
Arguments
nAn integer for the data set’s sample size
changepoint An integer for where the change point occurs
mean1 The mean prior to the change point
mean2 The mean after the change point
dist The function with which random data will be generated
meanparam A string for the parameter in dist representing the mean
... Other arguments to be passed to dist
Details
This function generates artificial change point data, where up to the specified change point the data
has one mean, and after the point it has a different mean. By default, the function simulates standard
Normal data with no change. If changepoint is NULL, then by default the change point will be at
about the middle of the data.
Value
A vector of the simulated data
Examples
CPAT:::rchangepoint(500)
CPAT:::rchangepoint(500, changepoint = 10, mean2 = 2, sd = 2)
CPAT:::rchangepoint(500, changepoint = 250, dist = rexp, meanparam = "rate",
mean1 = 1, mean2 = 2)
18 sim_de_stat
sim_de_stat Darling-Erdös Statistic Simulation
Description
Simulates multiple realizations of the Darling-Erdös statistic.
Usage
sim_de_stat(size, a = log, b = log, use_kernel_var = FALSE,
kernel = "ba", bandwidth = "and", n = 500, gen_func = rnorm,
args = NULL, parallel = FALSE)
Arguments
size Number of realizations to simulate
aThe function that will be composed wit l(x) = (2 log(x))1/2
bThe function that will be composed with u(x) = 2 log(x) + 1
2log(log(x)) −
1
2log(pi)
use_kernel_var Set to TRUE to use kernel-based long-run variance estimation (FALSE means this
is not employed)
kernel If character, the identifier of the kernel function as used in the cointReg (see
documentation for cointReg::getLongRunVar); if function, the kernel func-
tion to be used for long-run variance estimation (default is the Bartlett kernel in
cointReg); this parameter has no effect if use_kernel_var is FALSE
bandwidth If character, the identifier of how to compute the bandwidth as defined in the
cointReg package (see documentation for cointReg::getLongRunVar); if func-
tion, a function to use for computing the bandwidth; if numeric, the bandwidth
to use (the default behavior is to use the Andrews (1991) method, as used in
cointReg); this parameter has no effect if use_kernel_var is FALSE
nThe sample size for each realization
gen_func The function generating the random sample from which the statistic is computed
args A list of arguments to be passed to gen_func
parallel Whether to use the foreach and doParallel packages to parallelize simulation
(which needs to be initialized in the global namespace before use)
Details
If use_kernel_var is set to TRUE, long-run variance estimation using kernel-based techniques will
be employed; otherwise, a technique resembling standard variance estimation will be employed.
Any technique employed, though, will account for the potential break points, as described in Rice
et al. (). See the documentation for stat_de for more details.
The parameters kernel and bandwidth control parameters for long-run variance estimation using
kernel methods. These parameters will be passed directly to stat_de.
Value
A vector of simulated realizations of the Darling-Erdös statistic
sim_hs_stat 19
References
Andrews DWK (1991). “Heteroskedasticity and Autocorrelation Consistent Covariance Matrix
Estimation.” Econometrica,59(3), 817-858.
Rice G, Miller C, Horváth L (????). “A new class of change point test of Rényi type.” in-press.
Examples
CPAT:::sim_de_stat(100)
CPAT:::sim_de_stat(100, use_kernel_var = TRUE,
gen_func = CPAT:::rchangepoint,
args = list(changepoint = 250, mean2 = 1))
sim_hs_stat Hidalgo-Seo Statistic Simulation
Description
Simulates multiple realizations of the Hidalgo-Seo statistic.
Usage
sim_hs_stat(size, corr = TRUE, gen_func = rnorm, args = NULL,
n = 500, parallel = FALSE, use_kernel_var = FALSE, kernel = "ba",
bandwidth = "and")
Arguments
size Number of realizations to simulate
corr Whether long-run variance should be computed under the assumption of corre-
lated residuals
gen_func The function generating the random sample from which the statistic is computed
args A list of arguments to be passed to gen_func
nThe sample size for each realization
parallel Whether to use the foreach and doParallel packages to parallelize simulation
(which needs to be initialized in the global namespace before use)
use_kernel_var Set to TRUE to use kernel-based long-run variance estimation (FALSE means this
is not employed); TODO: NOT CURRENTLY IMPLEMENTED
kernel If character, the identifier of the kernel function as used in the cointReg (see
documentation for cointReg::getLongRunVar); if function, the kernel func-
tion to be used for long-run variance estimation (default is the Bartlett kernel in
cointReg); this parameter has no effect if use_kernel_var is FALSE;TODO:
NOT CURRENTLY IMPLEMENTED
bandwidth If character, the identifier of how to compute the bandwidth as defined in the
cointReg package (see documentation for cointReg::getLongRunVar); if func-
tion, a function to use for computing the bandwidth; if numeric, the bandwidth
to use (the default behavior is to use the Andrews (1991) method, as used in
cointReg); this parameter has no effect if use_kernel_var is FALSE;TODO:
NOT CURRENTLY IMPLEMENTED
20 sim_Vn
Details
If corr is TRUE, then the residuals of the data-generating process are assumed to be correlated and
the test accounts for this in long-run variance estimation; see the documentation for stat_hs for
more details. Otherwise, the sample variance is the estimate for the long-run variance, as described
in Hidalgo and Seo (2013).
Value
A vector of simulated realizations of the Hidalgo-Seo statistic
References
Andrews DWK (1991). “Heteroskedasticity and Autocorrelation Consistent Covariance Matrix
Estimation.” Econometrica,59(3), 817-858.
Hidalgo J, Seo MH (2013). “Testing for structural stability in the whole sample.” Journal of
Econometrics,175(2), 84 - 93. ISSN 0304-4076, doi: 10.1016/j.jeconom.2013.02.008,http:
//www.sciencedirect.com/science/article/pii/S0304407613000626.
Examples
CPAT:::sim_hs_stat(100)
CPAT:::sim_hs_stat(100, gen_func = CPAT:::rchangepoint,
args = list(changepoint = 250, mean2 = 1))
sim_Vn CUSUM Statistic Simulation (Assuming Variance)
Description
Simulates multiple realizations of the CUSUM statistic when the long-run variance of the data is
known.
Usage
sim_Vn(size, n = 500, gen_func = rnorm, sd = 1, args = NULL)
Arguments
size Number of realizations to simulate
nThe sample size for each realization
gen_func The function generating the random sample from which the statistic is computed
sd The square root of the second moment of the data
args A list of arguments to be passed to gen_func
Value
A vector of simulated realizations of the CUSUM statistic
sim_Vn_stat 21
Examples
CPAT:::sim_Vn(100)
CPAT:::sim_Vn(100, gen_func = CPAT:::rchangepoint,
args = list(changepoint = 250, mean2 = 1))
sim_Vn_stat CUSUM Statistic Simulation
Description
Simulates multiple realizations of the CUSUM statistic.
Usage
sim_Vn_stat(size, kn = function(n) { 1 }, tau = 0,
use_kernel_var = FALSE, kernel = "ba", bandwidth = "and",
n = 500, gen_func = rnorm, args = NULL, parallel = FALSE)
Arguments
size Number of realizations to simulate
kn A function returning a positive integer that is used in the definition of the trimmed
CUSUSM statistic effectively setting the bounds over which the maximum is
taken
tau The weighting parameter for the weighted CUSUM statistic (defaults to zero for
no weighting)
use_kernel_var Set to TRUE to use kernel-based long-run variance estimation (FALSE means this
is not employed)
kernel If character, the identifier of the kernel function as used in the cointReg (see
documentation for cointReg::getLongRunVar); if function, the kernel func-
tion to be used for long-run variance estimation (default is the Bartlett kernel in
cointReg); this parameter has no effect if use_kernel_var is FALSE
bandwidth If character, the identifier of how to compute the bandwidth as defined in the
cointReg package (see documentation for cointReg::getLongRunVar); if func-
tion, a function to use for computing the bandwidth; if numeric, the bandwidth
to use (the default behavior is to use the method described in (Andrews 1991),
as used in cointReg); this parameter has no effect if use_kernel_var is FALSE
nThe sample size for each realization
gen_func The function generating the random sample from which the statistic is computed
args A list of arguments to be passed to gen_func
parallel Whether to use the foreach and doParallel packages to parallelize simulation
(which needs to be initialized in the global namespace before use)
22 sim_Zn
Details
This differs from sim_Vn() in that the long-run variance is estimated with this function, while
sim_Vn() assumes the long-run variance is known. Estimation can be done in a variety of ways. If
use_kernel_var is set to TRUE, long-run variance estimation using kernel-based techniques will be
employed; otherwise, a technique resembling standard variance estimation will be employed. Any
technique employed, though, will account for the potential break points, as described in Rice et al.
(). See the documentation for stat_Vn for more details.
The parameters kernel and bandwidth control parameters for long-run variance estimation using
kernel methods. These parameters will be passed directly to stat_Vn.
Versions of the CUSUM statistic, such as the weighted or trimmed statistics, can be simulated with
the function by passing values to kn and tau; again, see the documentation for stat_Vn.
Value
A vector of simulated realizations of the CUSUM statistic
References
Andrews DWK (1991). “Heteroskedasticity and Autocorrelation Consistent Covariance Matrix
Estimation.” Econometrica,59(3), 817-858.
Rice G, Miller C, Horváth L (????). “A new class of change point test of Rényi type.” in-press.
Examples
CPAT:::sim_Vn_stat(100)
CPAT:::sim_Vn_stat(100, kn = function(n) {floor(0.1 * n)}, tau = 1/3,
use_kernel_var = TRUE, gen_func = CPAT:::rchangepoint,
args = list(changepoint = 250, mean2 = 1))
sim_Zn Rènyi-Type Statistic Simulation (Assuming Variance)
Description
Simulates multiple realizations of the Rènyi-type statistic when the long-run variance of the data is
known.
Usage
sim_Zn(size, kn, n = 500, gen_func = rnorm, args = NULL, sd = 1)
Arguments
size Number of realizations to simulate
kn A function returning a positive integer that is used in the definition of the Rènyi-
type statistic effectively setting the bounds over which the maximum is taken
nThe sample size for each realization
gen_func The function generating the random sample from which the statistic is computed
args A list of arguments to be passed to gen_func
sd The square root of the second moment of the data
sim_Zn_stat 23
Value
A vector of simulated realizations of the Rènyi-type statistic
Examples
CPAT:::sim_Zn(100, kn = function(n) {floor(log(n))})
CPAT:::sim_Zn(100, kn = function(n) {floor(log(n))},
gen_func = CPAT:::rchangepoint, args = list(changepoint = 250,
mean2 = 1))
sim_Zn_stat Rènyi-Type Statistic Simulation
Description
Simulates multiple realizations of the Rènyi-type statistic.
Usage
sim_Zn_stat(size, kn = function(n) { floor(sqrt(n)) },
use_kernel_var = FALSE, kernel = "ba", bandwidth = "and",
n = 500, gen_func = rnorm, args = NULL, parallel = FALSE)
Arguments
size Number of realizations to simulate
kn A function returning a positive integer that is used in the definition of the Rènyi-
type statistic effectively setting the bounds over which the maximum is taken
use_kernel_var Set to TRUE to use kernel-based long-run variance estimation (FALSE means this
is not employed)
kernel If character, the identifier of the kernel function as used in the cointReg (see
documentation for cointReg::getLongRunVar); if function, the kernel func-
tion to be used for long-run variance estimation (default is the Bartlett kernel in
cointReg); this parameter has no effect if use_kernel_var is FALSE
bandwidth If character, the identifier of how to compute the bandwidth as defined in the
cointReg package (see documentation for cointReg::getLongRunVar); if func-
tion, a function to use for computing the bandwidth; if numeric, the bandwidth
to use (the default behavior is to use the Andrews (1991) method, as used in
cointReg); this parameter has no effect if use_kernel_var is FALSE
nThe sample size for each realization
gen_func The function generating the random sample from which the statistic is computed
args A list of arguments to be passed to gen_func
parallel Whether to use the foreach and doParallel packages to parallelize simulation
(which needs to be initialized in the global namespace before use)
24 stat_de
Details
This differs from sim_Zn() in that the long-run variance is estimated with this function, while
sim_Zn() assumes the long-run variance is known. Estimation can be done in a variety of ways. If
use_kernel_var is set to TRUE, long-run variance estimation using kernel-based techniques will be
employed; otherwise, a technique resembling standard variance estimation will be employed. Any
technique employed, though, will account for the potential break points, as described in Rice et al.
(). See the documentation for stat_Zn for more details.
The parameters kernel and bandwidth control parameters for long-run variance estimation using
kernel methods. These parameters will be passed directly to stat_Zn.
Value
A vector of simulated realizations of the Rènyi-type statistic
References
Andrews DWK (1991). “Heteroskedasticity and Autocorrelation Consistent Covariance Matrix
Estimation.” Econometrica,59(3), 817-858.
Rice G, Miller C, Horváth L (????). “A new class of change point test of Rényi type.” in-press.
Examples
CPAT:::sim_Zn_stat(100)
CPAT:::sim_Zn_stat(100, kn = function(n) {floor(log(n))},
use_kernel_var = TRUE, gen_func = CPAT:::rchangepoint,
args = list(changepoint = 250, mean2 = 1))
stat_de Compute the Darling-Erdös Statistic
Description
This function computes the Darling-Erdös statistic.
Usage
stat_de(dat, a = log, b = log, estimate = FALSE,
use_kernel_var = FALSE, custom_var = NULL, kernel = "ba",
bandwidth = "and", get_all_vals = FALSE)
Arguments
dat The data vector
aThe function that will be composed with l(x) = (2 log x)1/2
bThe function that will be composed with u(x) = 2 log x+1
2log log x−1
2log π
estimate Set to TRUE to return the estimated location of the change point
use_kernel_var Set to TRUE to use kernel methods for long-run variance estimation (typically
used when the data is believed to be correlated); if FALSE, then the long-run vari-
ance is estimated using ˆσ2
T,t =T−1Pt
s=1 Xs−¯
Xt2+PT
s=t+1 Xs−˜
XT−t2,
where ¯
Xt=t−1Pt
s=1 Xsand ˜
XT−t= (T−t)−1PT
s=t+1 Xs
stat_hs 25
custom_var Can be a vector the same length as dat consisting of variance-like numbers
at each potential change point (so each entry of the vector would be the "best
estimate" of the long-run variance if that location were where the change point
occured) or a function taking two parameters xand kthat can be used to generate
this vector, with xrepresenting the data vector and kthe position of a potential
change point; if NULL, this argument is ignored
kernel If character, the identifier of the kernel function as used in cointReg (see getLongRunVar);
if function, the kernel function to be used for long-run variance estimation (de-
fault is the Bartlett kernel in cointReg)
bandwidth If character, the identifier for how to compute the bandwidth as defined in coin-
tReg (see getBandwidth); if function, a function to use for computing the band-
width; if numeric, the bandwidth value to use (the default is to use Andrews’
method, as used in cointReg)
get_all_vals If TRUE, return all values for the statistic at every tested point in the data set
Details
If ¯
AT(τ, tT)is the weighted and trimmed CUSUM statistic with weighting parameter τand trim-
ming parameter tT(see stat_Vn), then the Darling-Erdös statistic is
l(aT)¯
AT(1/2,1) −u(bT)
with l(x) = √2 log xand u(x) = 2 log x+1
2log log x−1
2log π(log xis the natural logarithm of
x). The parameter acorresponds to aTand bto bT; these are both log by default.
See (Rice et al. ) to learn more.
Value
If both estimate and get_all_vals are FALSE, the value of the test statistic; otherwise, a list that
contains the test statistic and the other values requested (if both are TRUE, the test statistic is in the
first position and the estimated changg point in the second)
References
Rice G, Miller C, Horváth L (????). “A new class of change point test of Rényi type.” in-press.
Examples
CPAT:::stat_de(rnorm(1000))
CPAT:::stat_de(rnorm(1000), use_kernel_var = TRUE, bandwidth = "nw", kernel = "bo")
stat_hs Compute the Hidalgo-Seo Statistic
Description
This function computes the Hidalgo-Seo statistic for a change in mean model.
26 stat_hs
Usage
stat_hs(dat, estimate = FALSE, corr = TRUE, get_all_vals = FALSE,
custom_var = NULL, use_kernel_var = FALSE, kernel = "ba",
bandwidth = "and")
Arguments
dat The data vector
estimate Set to TRUE to return the estimated location of the change point
corr If TRUE, the long-run variance will be computed under the assumption of corre-
lated residuals; ignored if custom_var is not NULL or use_kernel_var is TRUE
get_all_vals If TRUE, return all values for the statistic at every tested point in the data set
custom_var Can be a vector the same length as dat consisting of variance-like numbers
at each potential change point (so each entry of the vector would be the "best
estimate" of the long-run variance if that location were where the change point
occured) or a function taking two parameters xand kthat can be used to generate
this vector, with xrepresenting the data vector and kthe position of a potential
change point; if NULL, this argument is ignored
use_kernel_var Set to TRUE to use kernel methods for long-run variance estimation (typically
used when the data is believed to be correlated); if FALSE, then the long-run vari-
ance is estimated using ˆσ2
T,t =T−1Pt
s=1 Xs−¯
Xt2+PT
s=t+1 Xs−˜
XT−t2,
where ¯
Xt=t−1Pt
s=1 Xsand ˜
XT−t= (T−t)−1PT
s=t+1 Xs; if custom_var
is not NULL, this argument is ignored
kernel If character, the identifier of the kernel function as used in cointReg (see getLongRunVar);
if function, the kernel function to be used for long-run variance estimation (de-
fault is the Bartlett kernel in cointReg)
bandwidth If character, the identifier for how to compute the bandwidth as defined in coin-
tReg (see getBandwidth); if function, a function to use for computing the band-
width; if numeric, the bandwidth value to use (the default is to use Andrews’
method, as used in cointReg)
Details
For a data set xtwith nobservations, the test statistic is
max
1≤s≤n−1(LM(s)−Bn)/An
where ˆut=xt−¯x(¯xis the sample mean), an= (2 log log n)1/2,bn=a2
n−1
2log log log n−
log Γ(1/2),An=bn/a2
n,Bn=b2
n/a2
n,ˆ
∆ = ˆσ2=n−1Pn
t=1 ˆu2
t, and LM(s) = n(n−
s)−1s−1ˆ
∆−1(Ps
t=1 ˆut)2.
If corr is FALSE, then the residuals are assumed to be uncorrelated. Otherwise, the residuals are
assumed to be correlated and ˆ
∆ = ˆγ(0) + 2 Pb√nc
j=1 (1 −j
√n)ˆγ(j)with ˆγ(j) = 1
nPn−j
t=1 ˆutˆut+j.
This statistic was presented in (Hidalgo and Seo 2013).
Value
If both estimate and get_all_vals are FALSE, the value of the test statistic; otherwise, a list that
contains the test statistic and the other values requested (if both are TRUE, the test statistic is in the
first position and the estimated change point in the second)
stat_Vn 27
References
Hidalgo J, Seo MH (2013). “Testing for structural stability in the whole sample.” Journal of
Econometrics,175(2), 84 - 93. ISSN 0304-4076, doi: 10.1016/j.jeconom.2013.02.008,http:
//www.sciencedirect.com/science/article/pii/S0304407613000626.
Examples
CPAT:::stat_hs(rnorm(1000))
CPAT:::stat_hs(rnorm(1000), corr = FALSE)
stat_Vn Compute the CUSUM Statistic
Description
This function computes the CUSUM statistic (and can compute weighted/trimmed variants, de-
pending on the values of kn and tau).
Usage
stat_Vn(dat, kn = function(n) { 1 }, tau = 0, estimate = FALSE,
use_kernel_var = FALSE, custom_var = NULL, kernel = "ba",
bandwidth = "and", get_all_vals = FALSE)
Arguments
dat The data vector
kn A function corresponding to the trimming parameter tTin the trimmed CUSUM
variant; by default, is a function returning 1 (for no trimming)
tau The weighting parameter τfor the weighted CUSUM statistic; by default, is 0
(for no weighting)
estimate Set to TRUE to return the estimated location of the change point
use_kernel_var Set to TRUE to use kernel methods for long-run variance estimation (typically
used when the data is believed to be correlated); if FALSE, then the long-run vari-
ance is estimated using ˆσ2
T,t =T−1Pt
s=1 Xs−¯
Xt2+PT
s=t+1 Xs−˜
XT−t2,
where ¯
Xt=t−1Pt
s=1 Xsand ˜
XT−t= (T−t)−1PT
s=t+1 Xs
custom_var Can be a vector the same length as dat consisting of variance-like numbers
at each potential change point (so each entry of the vector would be the "best
estimate" of the long-run variance if that location were where the change point
occured) or a function taking two parameters xand kthat can be used to generate
this vector, with xrepresenting the data vector and kthe position of a potential
change point; if NULL, this argument is ignored
kernel If character, the identifier of the kernel function as used in cointReg (see getLongRunVar);
if function, the kernel function to be used for long-run variance estimation (de-
fault is the Bartlett kernel in cointReg)
bandwidth If character, the identifier for how to compute the bandwidth as defined in coin-
tReg (see getBandwidth); if function, a function to use for computing the band-
width; if numeric, the bandwidth value to use (the default is to use Andrews’
method, as used in cointReg)
get_all_vals If TRUE, return all values for the statistic at every tested point in the data set
28 stat_Zn
Details
The definition of the statistic is
T−1/2max
1≤t≤Tˆσ−1
t,T
t
X
s=1
Xs−t
T
T
X
s=1
A more general version is
T−1/2max
tT≤t≤T−tT
ˆσ−1
t,T t
TT−t
Tτ
t
X
s=1
Xs−t
T
T
X
s=1
The parameter kn corresponds to the trimming parameter tTand the parameter tau corresponds to
τ.
See (Rice et al. ) for more details.
Value
If both estimate and get_all_vals are FALSE, the value of the test statistic; otherwise, a list that
contains the test statistic and the other values requested (if both are TRUE, the test statistic is in the
first position and the estimated change point in the second)
References
Rice G, Miller C, Horváth L (????). “A new class of change point test of Rényi type.” in-press.
Examples
CPAT:::stat_Vn(rnorm(1000))
CPAT:::stat_Vn(rnorm(1000), kn = function(n) {0.1 * n}, tau = 1/2)
CPAT:::stat_Vn(rnorm(1000), use_kernel_var = TRUE, bandwidth = "nw", kernel = "bo")
stat_Zn Compute the Rényi-Type Statistic
Description
This function computes the Rényi-type statistic.
Usage
stat_Zn(dat, kn = function(n) { floor(sqrt(n)) }, estimate = FALSE,
use_kernel_var = FALSE, custom_var = NULL, kernel = "ba",
bandwidth = "and", get_all_vals = FALSE)
stat_Zn 29
Arguments
dat The data vector
kn A function corresponding to the trimming parameter tT; by default, the square
root function
estimate Set to TRUE to return the estimated location of the change point
use_kernel_var Set to TRUE to use kernel methods for long-run variance estimation (typically
used when the data is believed to be correlated); if FALSE, then the long-run vari-
ance is estimated using ˆσ2
T,t =T−1Pt
s=1 Xs−¯
Xt2+PT
s=t+1 Xs−˜
XT−t2,
where ¯
Xt=t−1Pt
s=1 Xsand ˜
XT−t= (T−t)−1PT
s=t+1 Xs; if custom_var
is not NULL, this argument is ignored
custom_var Can be a vector the same length as dat consisting of variance-like numbers
at each potential change point (so each entry of the vector would be the "best
estimate" of the long-run variance if that location were where the change point
occured) or a function taking two parameters xand kthat can be used to generate
this vector, with xrepresenting the data vector and kthe position of a potential
change point; if NULL, this argument is ignored
kernel If character, the identifier of the kernel function as used in cointReg (see getLongRunVar);
if function, the kernel function to be used for long-run variance estimation (de-
fault is the Bartlett kernel in cointReg)
bandwidth If character, the identifier for how to compute the bandwidth as defined in coin-
tReg (see getBandwidth); if function, a function to use for computing the band-
width; if numeric, the bandwidth value to use (the default is to use Andrews’
method, as used in cointReg)
get_all_vals If TRUE, return all values for the statistic at every tested point in the data set
Details
The definition of the statistic is
max
tT≤t≤T−tT
ˆσ−1
t,T
t−1
t
X
s=1
Xs−(T−t)−1
T
X
s=t+1
Xs
The parameter kn corresponds to the trimming parameter tT.
Value
If both estimate and get_all_vals are FALSE, the value of the test statistic; otherwise, a list that
contains the test statistic and the other values requested (if both are TRUE, the test statistic is in the
first position and the estimated change point in the second)
Examples
CPAT:::stat_Zn(rnorm(1000))
CPAT:::stat_Zn(rnorm(1000), kn = function(n) {floor(log(n))})
CPAT:::stat_Zn(rnorm(1000), use_kernel_var = TRUE, bandwidth = "nw",
kernel = "bo")
30 %s0%
%s% Concatenate (With Space)
Description
Concatenate and form strings (with space separation)
Usage
x %s% y
Arguments
xOne object
yAnother object
Value
A string combining xand ywith a space separating them
Examples
`%s%`<- CPAT:::`%s%`
"Hello" %s% "world"
%s0% Concatenate (Without Space)
Description
Concatenate and form strings (no space separation)
Usage
x %s0% y
Arguments
xOne object
yAnother object
Value
A string combining xand y
Examples
`%s0%`<- CPAT:::`%s0%`
"Hello" %s0% "world"
Index
∗Topic datasets
banks,5
ff,9
.onAttach,2
%s0%,30
%s%,30
Andrews.test,3
andrews_test,3,3
andrews_test_reg,3,4
banks,5
CPAT_startup_message,5
cpt_consistent_var,6
CUSUM.test,6
DE.test,7
dZn,8
ff,9
get_lrv_vec,10
getBandwidth,7,8,10,11,25–27,29
getLongRunVar,7,8,10,11,25–27,29
getLongRunWeights,10,10
HR.test,11
HS.test,12
lm,3,4
log,11
pdarling_erdos,7,13
phidalgo_seo,12,13
pkolmogorov,6,14
pZn,11,14
qdarling_erdos,15
qhidalgo_seo,15
qkolmogorov,16
qZn,16
rchangepoint,17
sim_de_stat,18
sim_hs_stat,19
sim_Vn,20
sim_Vn_stat,21
sim_Zn,22
sim_Zn_stat,23
sqrt,11
stat_de,7,18,24
stat_hs,12,20,25
stat_Vn,6,22,25,27
stat_Zn,11,24,28
uniroot,16,17
31

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