# stDistAutocop: Combined Test of Stationarity for Univariate Continuous Time... In npcp: Some Nonparametric CUSUM Tests for Change-Point Detection in Possibly Multivariate Observations

 stDistAutocop R Documentation

## 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 `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)
```

npcp documentation built on Feb. 16, 2023, 6:04 p.m.