cpAutocop | R Documentation |
Nonparametric test for change-point detection particularly sensitive to changes in the autocopula of univariate continuous observations. Approximate p-values for the test statistic are obtained by means of a multiplier approach. Details can be found in the first reference.
cpAutocop(x, lag = 1, b = NULL, bivariate = FALSE, weights = c("parzen", "bartlett"), m = 5, N = 1000, init.seq = NULL, include.replicates = FALSE)
x |
a one-column matrix containing continuous observations. |
lag |
an integer specifying at which lag to consider the
autocopula; the autocopula is a ( |
b |
strictly positive integer specifying the value of the
bandwidth parameter determining the serial dependence when
generating dependent multiplier sequences using the 'moving average
approach'; see Section 5 of the second reference. If set to
|
bivariate |
a logical specifying whether the test should focus
only on the bivariate margin of the ( |
weights |
a string specifying the kernel for creating the weights used in the generation of dependent multiplier sequences within the 'moving average approach'; see Section 5 of the second reference. |
m |
a strictly positive integer specifying the number of points of the uniform grid on (0,1) involved in the estimation of the bandwidth parameter; see Section 5 of the second reference. |
N |
number of multiplier replications. |
init.seq |
a sequence of independent standard normal variates of
length |
include.replicates |
a logical specifying whether the
object of |
The approximate p-value is computed as
(0.5 + sum(S[i] >= S, i=1, .., N)) / (N+1),
where S and S[i] denote the test statistic and a multiplier replication, respectively. This ensures that the approximate p-value is a number strictly between 0 and 1, which is sometimes necessary for further treatments.
An object of class
htest
which is a list,
some of the components of which are
statistic |
value of the test statistic. |
p.value |
corresponding approximate p-value. |
cvm |
the values of the |
b |
the value of parameter |
This is a tests for a continuous univariate time series.
A. Bücher, J.-D. Fermanian and I. Kojadinovic (2019), Combining cumulative sum change-point detection tests for assessing the stationarity of univariate time series, Journal of Time Series Analysis 40, pages 124-150, https://arxiv.org/abs/1709.02673.
A. Bücher and I. Kojadinovic (2016), A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing, Bernoulli 22:2, pages 927-968, https://arxiv.org/abs/1306.3930.
cpAutocov()
for a related test based on
the autocovariance.
## AR1 example n <- 200 k <- n/2 ## the true change-point x <- matrix(c(arima.sim(list(ar = -0.5), n = k), arima.sim(list(ar = 0.5), n = n - k))) cp <- cpAutocop(x) cp ## Estimated change-point which(cp$cvm == max(cp$cvm)) ## AR2 example n <- 200 k <- n/2 ## the true change-point x <- matrix(c(arima.sim(list(ar = c(0,-0.5)), n = k), arima.sim(list(ar = c(0,0.5)), n = n - k))) cpAutocop(x) cpAutocop(x, lag = 2) cpAutocop(x, lag = 2, bivariate = TRUE)
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