CUSUM_simple {memochange}

Simple test for change-in-mean under long memory

Description

This function performs a CUSUM test on a change-in-mean that is robust under long memory. It is based on the fractionally differenced series where the long-memory parameter is estimated by a consistent estimator. The function returns the test statistic as well as the p-value of the test.

Usage

CUSUM_simple(x, d)

Arguments

x

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

d

integer that specifies the long-memory parameter.

Value

Returns a numeric vector containing the test statistic and the p-value of the test.

Author(s)

Kai Wenger

References

Wenger, K. and Leschinski, C. and Sibbertsen, P. (2018): A simple test on structural change in long-memory time series. Economics Letters, 136, pp. 90-94.

See Also

CUSUMLM, CUSUMfixed

Examples

# set model parameters
T        <- 500
d        <- 0.2

set.seed(410)

# generate a fractionally integrated (long-memory) time series without a change in mean
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
CUSUM_simple(tseries, d_est)
CUSUM_simple(tseries2, 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 5% significance level.