cor_cusum: A CUSUM-type test to detect changes in the fluctuation.

In robcp: Robust Change-Point Tests

A CUSUM-type test to detect changes in the fluctuation.

Description

Performs a CUSUM-based test on changes in Spearman's rho or Kendall's tau.

Usage

cor_cusum(x, version = c("tau", "rho"), method = "kernel", control = list(), 
          fpc = TRUE, tol = 1e-08, plot = FALSE)

Arguments

x	time series (matrix or ts object with numeric/integer values).
version	version of the test. Either rho or tau.
method	method for estimating the long run variance.
control	a list of control parameters.
fpc	finite population correction (boolean).
tol	tolerance of the distribution function (numeric), which is used do compute p-values.
plot	should the test statistic be plotted (cf. plot.cpStat)? Boolean.

Details

The function perform a CUSUM-type test on changes in the fluctuation of a time series x. Formally, the hypothesis pair can be written as

H_0: ξ_1, ..., ξ_n

vs.

H_1: \exists k \in \{1, ..., n-1\}: ξ_k \neq ξ_{k+1}

where ξ_i is a fluctuation measure (either Spearman's rho or Kendall's tau) and n is the length of the time series. k is called a 'change point'.

The test statistic is computed using cor_stat and asymptotically follows a Kolmogorov distribution. To derive the p-value, the funtion pKSdist is used.

Value

A list of the class "htest" containing the following components:

statistic	return value of the function cor_stat.
p.value	p-value (numeric).
alternative	alternative hypothesis (character string).
method	name of the performed test (character string).
cp.location	index of the estimated change point location (integer).
data.name	name of the data (character string).
lrv	list containing the compontents method, param and value.

Author(s)

Sheila Görz

References

Wied, D., Dehling, H., Van Kampen, M., and Vogel, D. (2014). A fluctuation test for constant Spearman’s rho with nuisance-free limit distribution. Computational Statistics & Data Analysis, 76, 723-736.

Dürre, A. (2022+). "Finite sample correction for cusum tests", unpublished manuscript

See Also

cor_stat, lrv, pKSdist

Examples

### first: gerenate a time series with a burn-in period of m and a change point k
require(mvtnorm)
n <- 500
m <- 100
N <- n + m
k <- m + floor(n * 0.5)
n1 <- N - k

## Spearman's rho:
rho <- c(0.4, -0.9)
  
# serial dependence:
theta1 <- 0.3
theta2 <- 0.2
theta <- cbind(c(theta1, 0), c(0, theta2))
q <- rho * sqrt( (theta1^2 + 1) * (theta2^2 + 1) / (theta1 * theta2 + 1))
# shape matrices of the innovations:
S0 <- cbind(c(1, q[1]), c(q[1], 1))
S1 <- cbind(c(1, q[2]), c(q[2], 1))

e0 <- rmvt(k, S0, 5)
e1 <- rmvt(n1, S1, 5)
e <- rbind(e0, e1)
# generate the data:
x <- matrix(numeric(N * 2), ncol = 2)
x[1, ] <- e[1, ]
invisible(sapply(2:N, function(i) x[i, ] <<- e[i, ] + theta %*% e[i-1, ]))
x <- x[-(1:m), ]

cor_cusum(x, "rho")


## Kendall's tau
S0 <- cbind(c(1, rho[1]), c(rho[1], 1))
S1 <- cbind(c(1, rho[2]), c(rho[2], 1))
e0 <- rmvt(k, S0, 5)
e1 <- rmvt(n1, S1, 5)
e <- rbind(e0, e1)
x <- matrix(numeric(N * 2), ncol = 2)
x[1, ] <- e[1, ]
# AR(1):
invisible(sapply(2:N, function(i) x[i, ] <<- 0.8 * x[i-1, ] + e[i, ]))
x <- x[-(1:m), ]

cor_cusum(x, version = "tau")

robcp documentation built on Sept. 16, 2022, 5:05 p.m.