CUSUMLM: CUSUM long memory test for a single change in the mean of a...
In memochange: Testing for Structural Breaks under Long Memory and Testing for Changes in Persistence

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 `G` that approximates the short run dynamics of the time series at the origin. The same bandwidth should be used that is applied to estimate `d` before. See Wenger, Leschinski, Sibbertsen (2018) for details.
`tau`	integer that defines the search area, which is `[tau,1-tau]`. Default is `tau=0.15` as suggested by Andrews (1993).

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.

CUSUMfixed, CUSUM_simple

# 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.