wbsts (version 2.1)

tau.fun: Universal thresholds

Description

The function returns \(C^{(i)}\). \(C^{(i)}\) tends to increase as we move to coarser scales due to the increasing dependence in the wavelet periodogram sequences. Since the method applies to non-dyadic structures it is reasonable to propose a general rule that will apply in most cases. To accomplish this the \(C^{(i)}\) are obtained for \(T=50,100,...,6000\). Then, for each scale \(i\) the following regression is fitted

\(C^{(i)}=c_0^{(i)}+c_1^{(i)} T+ c_2^{(i)} \frac{1}{T} + c_3^{(i)} T^2 +\varepsilon.\)

The adjusted \(R^2\) was above 90% for all the scales. Having estimated the values for \(\hat{c}_0^{(i)}, \hat{c}_1^{(i)}, \hat{c}_2^{(i)}, \hat{c}_3^{(i)}\) the values can be retrieved for any sample size \(T\).

Usage

tau.fun(y)

Arguments

y

A time series

Value

Thresholds for every wavelet scale

References

P. Fryzlewicz (2014), Wild Binary Segmentation for multiple change-point detection. Annals of Statistics, 42, 2243-2281. (http://stats.lse.ac.uk/fryzlewicz/wbs/wbs.pdf)

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 {
##not run##
#cps=c(400,470)
#set.seed(101)
#y=sim.pw.ar(N =2000,sd_u = 1,b.slope=c(0.4,-0.6,0.5),br.loc=cps)[[2]]
#tau.fun(y) is the default value for C_i
##Binary segmentation
#wbs.lsw(y,M=1)$cp.aft
##Wild binary segmentation
#wbs.lsw(y,M=3500)$cp.aft

# }