snsupwald: Self-normalized sup Wald test for a single change in the mean...

In memochange: Testing for Structural Breaks under Long Memory and Testing for Changes in Persistence

Description

This function performs a sup Wald test for a change-in-mean that is robust under long memory. In contrast to a standard sup Wald 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

snsupwald(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.

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.

Shao, X. (2011): A simple test of changes in mean in the possible presence of long-range dependence. Journal of Time Series Analysis, 32, pp. 598-606.

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

See Also

fixbsupw, snwilcoxon

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
snsupwald(tseries, d=d_est)
snsupwald(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.

Example output

          90%           95%           99% Teststatistic 
       31.984        37.412        49.325        18.607 
          90%           95%           99% Teststatistic 
       39.338        46.646        61.826        55.678 

memochange documentation built on July 27, 2020, 1:09 a.m.