Description Usage Arguments Details Value Author(s) References See Also Examples
This function performs a family of CUSUM tests for a changeinmean that are robust under long memory. They apply nonparametric kernelbased fixedb and fixedm longrun variance estimators in the denominator of the test statistics. The function returns the test statistic as well as critical values.
1  CUSUMfixed(x, d, procedure, bandw, tau = 0.15)

x 
the univariate numeric vector to be investigated. Missing values are not allowed. 
d 
integer that specifies the longmemory parameter. 
procedure 
string that specifies whether the CUSUM fixedb or fixedm type A or type B tests are used. It can be chosen between

bandw 
integer that determines the bandwidth used for estimation of the longrun variance. For the fixedb tests 
tau 
integer that defines the search area, which is 
Note that the critical values are generated for tau=0.15
using the Bartlett kernel for the fixedb tests or averaging the first m periodogram
ordinates (which corresponds to the Daniell kernel) for the fixedm tests.
Returns a numeric vector containing the test statistic and the corresponding critical values of the test.
Kai Wenger
Wenger, K. and Leschinski, C. (2019): Changeinmean tests in longmemory time series: a review of recent developments. AStA Advances in Statistical Analysis, 103:2, pp. 237256.
Hualde, J. and Iacone, F. (2017): Fixed bandwidth asymptotics for the studentized mean of fractionally integrated processes. Economics Letters, 150, pp. 3943.
Andrews, D. W. K. (1993): Tests for Parameter Instability and Structural Change With Unknown Change Point. Econometrica, 61, pp. 821856.
CUSUMLM
, CUSUM_simple
, fixbsupw
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 29 30 31 32 33 34 35  # set model parameters
T < 500
d < 0.2
set.seed(410)
# generate a fractionally integrated (longmemory) time series
tseries < fracdiff::fracdiff.sim(n=T, d=d)$series
# generate a fractionally integrated (longmemory) time series
# with a change in mean in the middle of the series
changep < c(rep(0,T/2), rep(1,T/2))
tseries2 < tseries+changep
# estimate the longmemory parameter of both series via local
# Whittle approach. The bandwidth to estimate d is chosen
# as T^0.65, which is usual in literature
d_est < LongMemoryTS::local.W(tseries, m=floor(1+T^0.65))$d
d_est2 < LongMemoryTS::local.W(tseries2, m=floor(1+T^0.65))$d
# perform the different types of the test on both time series
CUSUMfixed(tseries, d=d_est, procedure="CUSUMfixedb_typeA", bandw=0.1)
CUSUMfixed(tseries, d=d_est, procedure="CUSUMfixedb_typeB", bandw=0.1)
CUSUMfixed(tseries, d=d_est, procedure="CUSUMfixedm_typeA", bandw=10)
CUSUMfixed(tseries, d=d_est, procedure="CUSUMfixedm_typeB", bandw=10)
CUSUMfixed(tseries2, d=d_est2, procedure="CUSUMfixedb_typeA", bandw=0.1)
CUSUMfixed(tseries2, d=d_est2, procedure="CUSUMfixedb_typeB", bandw=0.1)
CUSUMfixed(tseries2, d=d_est2, procedure="CUSUMfixedm_typeA", bandw=10)
CUSUMfixed(tseries2, d=d_est2, procedure="CUSUMfixedm_typeB", bandw=10)
# For the series with no change in mean all tests do not reject
# the null hypothesis of a constant mean across time at
# any reasonable significance level.
# For the series with a change in mean all tests reject the
# null hypothesis at a 1% significance level.

90% 95% 99% Teststatistic
1.075 1.400 1.426 0.880
90% 95% 99% Teststatistic
1.720 1.993 2.593 0.985
90% 95% 99% Teststatistic
1.294 1.415 1.614 0.830
90% 95% 99% Teststatistic
1.562 1.785 2.247 0.883
90% 95% 99% Teststatistic
1.194 1.378 1.420 1.555
90% 95% 99% Teststatistic
2.346 2.748 3.612 4.613
90% 95% 99% Teststatistic
1.549 1.664 1.844 2.033
90% 95% 99% Teststatistic
2.221 2.565 3.248 4.133
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