wbsts (version 2.1)

cr.rand.max.inner.prod: The value that maximises the random CUSUM statistic across all the scales

Description

The function finds the value which yields the maximum inner product with the input time series (CUSUM) located between \(100(1-p)\%\) and \(100p\%\) of their support across all the wavelet periodogram scales.

Usage

cr.rand.max.inner.prod(XX,Ts,C_i,epp,M = 0,Plot = FALSE,cstar=0.95)

Arguments

XX

The wavelet periodogram.

Ts

The sample size of the series.

C_i

The CUSUM threshold.

epp

A minimum adjustment for the bias present in \(E^{(i)}_{t,T}\).

M

Number of random CUSUM to be generated.

Plot

Plot the threhsold CUSUM statistics across the wavelet scales.

cstar

A scalar in (0.67,1]

Value

1

Candidate change point

2

The maximum CUSUM value

3

The starting point \(s\) of the favourable draw

4

The ending point \(e\) of the favourable draw

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References

K. Korkas and P. Fryzlewicz (2017), Multiple change-point detection for non-stationary time series using Wild Binary Segmentation. Statistica Sinica, 27, 287-311. (http://stats.lse.ac.uk/fryzlewicz/WBS_LSW/WBS_LSW.pdf)

Examples

# NOT RUN {
#cps=seq(from=1000,to=2000,by=200)
#y=sim.pw.arma(N =3000,sd_u = c(1,1.5,1,1.5,1,1.5,1),
#b.slope=rep(0.99,7),b.slope2 = rep(0.,7), mac = rep(0.,7),br.loc = cps)[[2]]
#z=ews.trans(y,scales=c(11,9,8,7,6))
#out=cr.rand.max.inner.prod(z, Ts = length(y),C_i = tau.fun(y), 
#epp = rep(32,5), M = 2000, cstar = 0.75, Plot = 1)
#abline(v=cps,col="red")
# }