stDistAutocop {npcp}

Combined Test of Stationarity for Univariate Continuous Time Series Sensitive to Changes in the Distribution Function and the Autocopula

Description

A nonparametric test of stationarity for univariate continuous time series resulting from a combination à la Fisher of the change-point test sensitive to changes in the distribution function implemented in cpDist() and the change-point test sensitive to changes in the autcopula implemented in cpAutocop(). Approximate p-values are obtained by combining two multiplier resampling schemes. Details can be found in the first reference.

Usage

stDistAutocop(x, lag = 1, b = NULL, pairwise = FALSE,
              weights = c("parzen", "bartlett"), m = 5, N = 1000)

Arguments

x

a one-column matrix containing continuous observations.

lag

an integer specifying at which lag to consider the autocopula; the autcopula is a (lag+1)-dimensional copula.

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 NULL, b will be estimated using the function bOptEmpProc(); see the first reference.

pairwise

a logical specifying whether the test should focus only on the bivariate margins of the (lag+1)-dimensional autocopula.

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.

Details

The testing procedure is described in detail in the second section of the first reference.

Value

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 à Fisher.

component.p.values

p-values of the component tests arising in the combination.

b

the value of parameter b.

Note

This is a test for continuous univariate time series.

References

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.

See Also

see cpDist() and cpAutocop() for the component tests.

Examples

## AR1 example
n <- 200
k <- n/2 ## the true change-point
x <- matrix(c(arima.sim(list(ar = -0.1), n = k),
              arima.sim(list(ar = 0.5), n = n - k)))
stDistAutocop(x)

## AR2 example
n <- 200
k <- n/2 ## the true change-point
x <- matrix(c(arima.sim(list(ar = c(0,-0.1)), n = k),
              arima.sim(list(ar = c(0,0.5)), n = n - k)))
## Not run: 
stDistAutocop(x)
stDistAutocop(x, lag = 2)
## End(Not run)
stDistAutocop(x, lag = 2, pairwise = TRUE)