Description Usage Arguments Details Value Author(s) References See Also Examples

This function performs a modified CUSUM test for a change-in-mean that is robust under long memory. It replaces the standardization as well as the long-run variance estimator compared to the standard CUSUM test. The function returns the test statistic as well as critical values.

1 | ```
CUSUMLM(x, d, delta, tau = 0.15)
``` |

`x` |
the univariate numeric vector to be investigated. Missing values are not allowed. |

`d` |
integer that specifies the long-memory parameter. |

`delta` |
integer that determines the bandwidth that is used to estimate the constant |

`tau` |
integer that defines the search area, which is |

Note that the critical values are generated for `tau=0.15`

.

Returns a numeric vector containing the test statistic and the corresponding critical values of the test.

Kai Wenger

Wenger, K. and Leschinski, C. and Sibbertsen, P. (2018): Change-in-mean tests in long-memory time series: a review of recent developments. AStA Advances in Statistical Analysis, 103:2, pp. 237-256.

Wang, L. (2008): Change-in-mean problem for long memory time series models with applications. Journal of Statistical Computation and Simulation, 78:7, pp. 653-668.

Horvath, L. and Kokoszka, P. (1997): The effect of long-range dependence on change-point estimators. Journal of Statistical Planung and Inference, 64, pp. 57-81.

Andrews, D. W. K. (1993): Tests for Parameter Instability and Structural Change With Unknown Change Point. Econometrica, 61, pp. 821-856.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 | ```
# set model parameters
T <- 500
d <- 0.2
set.seed(410)
# generate a fractionally integrated (long-memory) time series
tseries <- fracdiff::fracdiff.sim(n=T, d=d)$series
# generate a fractionally integrated (long-memory) time series
# with a change in mean in the middle of the series
changep <- c(rep(0,T/2), rep(1,T/2))
tseries2 <- tseries+changep
# estimate the long-memory parameter of both series via local
# Whittle approach. The bandwidth to estimate d is chosen
# as T^0.65, which is usual in literature
d_est <- LongMemoryTS::local.W(tseries, m=floor(1+T^0.65))$d
d_est2 <- LongMemoryTS::local.W(tseries2, m=floor(1+T^0.65))$d
# perform the test on both time series
CUSUMLM(tseries, delta=0.65, d=d_est)
CUSUMLM(tseries2, delta=0.65, d=d_est2)
# For the series with no change in mean the test does not
# reject the null hypothesis of a constant mean across time
# at any reasonable significance level.
# For the series with a change in mean the test rejects the
# null hypothesis at a 1% significance level.
``` |

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