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

This function performs a sup-Wald test on a change-in-mean, which is standardized by a non-parametric kernel-based long-run variance estimator. Therefore, the test is robust under long-memory. The function returns the test statistic as well as critical values.

1 | ```
fixbsupw(x, d, bandw = 0.1, tau = 0.15)
``` |

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

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

`bandw` |
integer that determines the bandwidth parameter for the long-run variance estimator. It can take values in the range |

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

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

using the Bartlett kernel.

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

Kai Wenger

Iacone, F. and Leybourne, S. J. and Taylor, R. A. M. (2014): A fixed-b Test for a Break in Level at an unknown Time under Fractional Integration. Journal of Time Series Analysis, 35, pp. 40-54.

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
fixbsupw(tseries, d=d_est)
fixbsupw(tseries2, 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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