| Type: | Package |
| Title: | Change Point Tests for Joint Distributions and Copulas |
| Version: | 0.1.7 |
| Maintainer: | Bruno N Remillard <bruno.remillard@hec.ca> |
| Description: | Change point tests for joint distributions and copulas using pseudo-observations with multipliers or bootstrap. The processes used here have been defined in Bucher, Kojadinovic, Rohmer & Segers <doi:10.1016/j.jmva.2014.07.012> and Nasri & Remillard <doi:10.1016/j.jmva.2019.03.002>. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| LazyData: | true |
| Depends: | R (≥ 3.5.0), doParallel, parallel, foreach, stats |
| RoxygenNote: | 7.3.2 |
| NeedsCompilation: | yes |
| Packaged: | 2024-09-23 14:42:37 UTC; 49009427 |
| Author: | Bouchra R Nasri [aut], Bruno N Remillard [aut, cre, cph] |
| Repository: | CRAN |
| Date/Publication: | 2024-09-23 15:00:07 UTC |
Function to perform traditional bootstrap for changepoint
Description
This function select a bootstrap sample of indices and compute the Cramer-von Mises and Kolmogorov-Smirnov test statistics for changepoint
Usage
bootstrapfun(X, n)
Arguments
X |
n x d matrix of pseudo-observations; |
n |
length of the series. |
Value
cvm |
simulated value of the Cramer-von Mises statistic |
ks |
simulated value of the Kolmogorov-Smirnov statistic |
Function to compute changepoint statistics
Description
This function is used to compute the Cramer-von Mises and Kolmogorov-Smirnov test statistics for changepoint
Usage
cpCopDStats(U, n, d)
Arguments
U |
n x d matrix of pseudo-observations |
n |
length of the series |
d |
number of variables |
Value
statS |
Values of the Cramer-von Mises statistics |
statT |
Values of the Kolmogorov-Smirnov statistics |
Author(s)
Bouchra R Nasri and Bruno N Remillard, August 6, 2020
Function to compute bootstrapped changepoint statistics
Description
This function compute bootstrapped multipliers values for the Cramer-von Mises and Kolmogorov-Smirnov test statistics for changepoint
Usage
cpCopMultStats(MC, xi, s, n)
Arguments
MC |
matrix needed for multipliers |
xi |
multipliers |
s |
sequence of normalized values in (0,1) |
n |
length of the series |
Value
statS |
Simulated values of the Cramer-von Mises statistics |
statT |
Simulated values of the Kolmogorov-Smirnov statistics |
Author(s)
Bouchra R Nasri and Bruno N Remillard, August 6, 2020
Function to compute the bootstrapped statistics for the BKRS process
Description
This function is used to compute bootstrapped statistics from the BKRS process in the non-sequential case
Usage
cpCopMultStatsBKRSNonSeq(MC, MC1, grad, xi, s, n, d)
Arguments
MC |
matrix needed for multipliers |
MC1 |
matrices needed for multipliers |
grad |
gradient of the copula |
xi |
multipliers |
s |
sequence of normalized values in (0,1) |
n |
length of the series |
d |
number of variables |
Value
statS |
Values of the Cramer-von Mises statistics |
statT |
Values of the Kolmogorov-Smirnov statistics |
Author(s)
Bouchra R Nasri and Bruno N Remillard, August 6, 2020
Function to compute the statistics for the BKRS process
Description
This function is used to compute bootstrapped statistics from the BKRS process in the sequential case
Usage
cpCopMultStatsBKRSSeq(U, grad, xi, n, d)
Arguments
U |
matrix needed for multipliers |
grad |
gradient of the copula |
xi |
multipliers |
n |
length of the series |
d |
number of variables |
Value
statS |
Values of the Cramer-von Mises statistics |
statT |
Values of the Kolmogorov-Smirnov statistics |
Author(s)
Bouchra R Nasri and Bruno N Remillard, August 6, 2020
Function to compute the statistics for the traditional empirical process
Description
This function is used to compute the empirical process used in the changepoint tests
Usage
cpCopStats(x)
Arguments
x |
n x d matrix of pseudo-observations |
Value
M |
Matrix for the cdf |
statS |
Values of the Cramer-von Mises statistics |
statT |
Values of the Kolmogorov-Smirnov statistics |
Author(s)
Bouchra R Nasri and Bruno N Remillard, August 6, 2020
Function to compute the statistics for the BKRS process
Description
This function is used to compute the empirical process used in the changepoint tests
Usage
cpCopStatsBKRS(x, n, d)
Arguments
x |
n x d matrix of pseudo-observations |
n |
length of the series |
d |
number of variables |
Value
MC |
Matrix needed for multipliers |
MC1 |
Matrices needed for multipliers |
grad1 |
Esatimated gradient of the copula |
Author(s)
Bouchra R Nasri and Bruno N Remillard, August 6, 2020
Function to compute the empirical cdf at given points
Description
This function is used to compute the empirical process used in the changepoint tests
Usage
emp.cdf(x, u)
Arguments
x |
n x d matrix of pseudo-observations |
u |
evaluation points of the cdf |
Value
M |
Values of the empirical process |
cumsum |
Associated cumulativ sums |
Author(s)
Bouchra R Nasri and Bruno N Remillard, August 6, 2020
Function to perform multiplier bootstrap for changepoint
Description
This function simulates a random sample of Gaussian multipliers null hypothesis of a Gaussian HMM and compute the Cramer-von Mises and Kolmogorov-Smirnov test statistics.
Usage
multiplierDNonSeqfun(MC, MC1, grad, s, n, d)
Arguments
MC |
matrix needed for multipliers |
MC1 |
matrices needed for multipliers |
grad |
gradient of the copula |
s |
sequence of normalized values in (0,1) |
n |
length of the series |
d |
number of variables |
Value
cvm |
simulated value of the Cramer-von Mises statistic |
ks |
simulated value of the Kolmogorov-Smirnov statistic |
Author(s)
Bouchra R Nasri and Bruno N Remillard, August 6, 2020
References
Nasri, B. R. Remillard, B., & Bahraoui, T. (2022).
Function to perform multiplier bootstrap for changepoint
Description
This function simulates a random sample of Gaussian multipliers null hypothesis of a Gaussian HMM and compute the Cramer-von Mises and Kolmogorov-Smirnov test statistics.
Usage
multiplierDSeqfun(U, grad, n, d)
Arguments
U |
matrix needed for multipliers |
grad |
gradient of the copula |
n |
length of the series |
d |
number of variables. |
Value
cvm |
simulated value of the Cramer-von Mises statistic |
ks |
simulated value of the Kolmogorov-Smirnov statistic |
Author(s)
Bouchra R Nasri and Bruno N Remillard, August 6, 2020
References
Nasri, B. R. Remillard, B., & Bahraoui, T. (2022).
Function to perform multiplier bootstrap for changepoint
Description
This function simulates a random sample of Gaussian multipliers null hypothesis of a Gaussian HMM and compute the Cramer-von Mises and Kolmogorov-Smirnov test statistics.
Usage
multiplierfun(MC, s, n)
Arguments
MC |
n x n matrix = MM - C, with MM[i,j] = 1(Xi <= Xj) and C=mean(M[,j]); |
n |
length of the series. |
Value
cvm |
simulated value of the Cramer-von Mises statistic |
ks |
simulated value of the Kolmogorov-Smirnov statistic |
Author(s)
Bouchra R Nasri and Bruno N Remillard, August 6, 2020
References
Chapter 8 of B. Remillard (2013). Statistical Methods for Financial Engineering, Chapman and Hall/CRC Financial Mathematics Series, Taylor & Francis.
Pseudo-observations
Description
Pseudo-observations used in Nasri, Remillard, Bahraoui (2021). The values represent conditional cdfs of Gaussian HMM models applied to log-returns of Nasdaq and Dow Jones Industrial indexes from 2007 and 2008. If the models are correct, the pseudo-observations should be almost iid with uniform distribution.
Usage
data(pseudos)Format
Pseudo-observations from Gaussian HMM models with 3 regimes for log-returns of the to Nasdaq index and Dow Jones Industrial indexes from 2007 and 2008.
1st column: pseudo-observations of a Gaussian HMM model with 3 regimes applied to the Nasdaq log-returns.
2nd column: pseudo-observations of a Gaussian HMM model with 3 regimes applied to the Dow Jones Industrial log-returns.
Function to perform changepoint tests with multiplier bootstrap using the usual sequential process
Description
This function compute the Cramer-von Mises and Kolmogorov-Smirnov test statistics based on the new sequential process of Bucher et al (2014), using multipliers and parallel computing.
Usage
test.change.point(
x,
N = 1000,
n_cores = 2,
boot.method = "multipliers",
est = FALSE
)
Arguments
x |
(n x d) matrix of data (observations or pseudo-observations, including residuals), d>=1 |
N |
number of multipliers samples to compute the P-value |
n_cores |
number of cores for parallel computing (default = 2) |
boot.method |
bootstrapping method: 'multipliers' (default, fastest) or 'bootstrap' |
est |
if TRUE, tau is estimated (default = FALSE) |
Value
CVM |
Cramer-von Mises statistic |
KS |
Kolmogorov-Smirnov statistic |
pvalueCVM |
Pvalue for the Cramer-von Mises statistic |
pvalueKS |
Pvalue for theKolmogorov-Smirnov statistic |
tauCVM |
Estimated changepoint using the Cramer-von Mises statistic |
tauKS |
Estimated changepoint using the Kolmogorov-Smirnov statistic |
Author(s)
Bouchra R Nasri and Bruno N Remillard, August 6, 2020
References
Nasri, B. R. Remillard, B., & Bahraoui, T. (2022). Change-point problems for multivariate time series using pseudo-observations, J. Multivariate Anal., 187, 104857.
Examples
x=matrix(rnorm(600),ncol=3)
out = test.change.point(x)
Function toperform changepoint test for the copula with multiplier bootstrap using for changepoint the new sequential process of Bucher et al (2014)
Description
This function compute the Cramer-von Mises and Kolmogorov-Smirnov test statistics based on the new sequential process of Bucher et al (2014), using multipliers and parallel computing. Two methods of bootstrapping are used: non-sequential (fastest) and sequential. Both methods yields basically the same P-valueas.
Usage
test.change.point.copula.BKRS(
x,
N = 1000,
n_cores = 2,
method = "nonseq",
est = FALSE
)
Arguments
x |
(n x d) matrix of data (observations or pseudo-observations, including residuals), d >=2 |
N |
number of multipliers samples to compute the P-value |
n_cores |
number of cores for parallel computing (default = 2) |
method |
'nonseq' (default) or 'seq' |
est |
if TRUE, tau is estimated (default = FALSE) |
Value
CVM |
Cramer-von Mises statistic |
KS |
Kolmogorov-Smirnov statistic |
pvalueCVM |
Pvalue for the Cramer-von Mises statistic |
pvalueKS |
Pvalue for theKolmogorov-Smirnov statistic |
tauCVM |
Estimated changepoint using the Cramer-von Mises statistic |
tauKS |
Estimated changepoint using the Kolmogorov-Smirnov statistic |
Author(s)
Bouchra R Nasri and Bruno N Remillard, August 6, 2020
References
Nasri, B. R. Remillard, B., & Bahraoui, T. (2022). Change-point problems for multivariate time series using pseudo-observations, J. Multivariate Anal., 187, 104857.
Bucher, A., Kojadinovic, I., Rohmer, T., & Segers, J. (2014). Detecting changes in cross-sectional dependence in multivariate time series, J. Multiv. Anal., 132, 111–128.
Examples
x<-matrix(rnorm(100),ncol=2)
out = test.change.point.copula.BKRS(x)