memochange (version 1.1.2)

fixbsupw: Fixed-b sup Wald test for a single change in the mean of a long-memory time series.

Description

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.

Usage

fixbsupw(x, d, bandw = 0.1, tau = 0.15)

Value

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

Arguments

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 bandw=[0.05,0.1,0.2]. Default is bandw=0.1, which is suggested by Iacone, Leybourne and Taylor (2014).

tau

integer that defines the search area, which is [tau,1-tau]. Default is tau=0.15 as suggested by Andrews (1993).

Author

Kai Wenger

Details

Note that the critical values are generated for tau=0.15 using the Bartlett kernel.

References

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.

See Also

CUSUMfixed, snsupwald

Examples

# 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.