snwilcoxon {memochange}

Self-normalized Wilcoxon test for a single change in the mean of a long-memory time series.

Description

This function performs a Wilcoxon test for a change-in-mean that is robust under long memory. In contrast to a standard Wilcoxon test it applies a self-normalization approach to estimate the long-run variance. The function returns the test statistic as well as critical values.

Usage

snwilcoxon(x, d, tau = 0.15)

Arguments

x

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

d

integer that specifies the long-memory parameter.

tau

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

Details

Note that the critical values are generated for tau=0.15. Furthermore, it is assumed that we have a 1st-order Hermite process. For details see Betken (2016).

Value

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

Author(s)

Kai Wenger

References

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.

Betken, A. (2016): Testing for change-points in long-range dependent time series by means of a self-normalized wilcoxon test. Journal of Time Series Analysis, 37, pp. 785-908.

Andrews, D. W. K. (1993): Tests for Parameter Instability and Structural Change With Unknown Change Point. Econometrica, 61, pp. 821-856.

See Also

wilcoxonLM, 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
snwilcoxon(tseries, d=d_est)
snwilcoxon(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.