test.once.psi {OLCPM}

test single change point for matrix-valued online data given rolling eigenvalue series

Description

This function tests single change point for matrix-valued online time series, under a two-way factor structure, given the transformed eigenvalue series.

Usage

test.once.psi(m = 20, psi, method = "ps", eta = 0.25, cv = 2.386)

Arguments

m

a positive integer (>1) indicating the bandwidth of the rolling windom.

psi

the transformed eigenvalue series, produced by gen.psi.tau.flat or gen.psi.tau.proj, with length T-m.

method

indicating the test statistic, “ps” for the partial-sum method, while others for the worst-case method.

eta

a number between [0,1), indicating the parameter \eta used in the partial-sum statistic.

cv

critical value, related to the significance level and test statistic. The default cv is from Horvath et al. (2004), and only works for \eta=0.25 or \eta=0.75. For other cases, generate the critical value first by function getcv. Note that for the partial-sum statistic with \eta not equal to 0.5, the critical values are approximated by simulated data, thus can be slightly different from those in Horvath et al. (2004).

Details

See He et al. (2021).

Value

a list containing:

test

a logical value. 1 indicating the existence of change point, 0 indicating no change point.

loc

an integer larger than m, indicating the location of change point; or NA when no change point is reported.

Author(s)

Yong He, Xinbing Kong, Lorenzo Trapani, Long Yu

References

Horvath L, Huskova M, Kokoszka P, et al (2004). Monitoring changes in linear models. Journal of statistical Planning and Inference, 126(1): 225-251.

He Y, Kong X, Trapani L, & Yu L(2021). Online change-point detection for matrix-valued time series with latent two-way factor structure. arXiv preprint, arXiv:2112.13479.

Examples

k1=3
k2=3
epsilon=0.05
Sample_T=50
p1=40
p2=20
kmax=8
r=8
m=p2

# generate data
Y=gen.data(Sample_T,p1,p2,k1,k2,tau=0.5,change=1,pp=0.5)

# calculate delta
temp=log(p1)/log(m*p2)
delta=epsilon*(temp<=0.5)+(epsilon+1-1/(2*temp))*(temp>0.5)

# calculate psi.tau
psi1=gen.psi.tau.proj(Y,k1+1,m,delta,r,kmax)
psi2=gen.psi.tau.flat(Y,k1+1,m,delta,r)

# calculate cv for "ps" with eta=0.45 and "wc"
cv1=getcv(0.05,method="ps",eta=0.45)
cv2=getcv(0.05,method="wc")


# test with psi1
test.once.psi(m,psi1[,3],method="ps",eta=0.45,cv1)

test.once.psi(m,psi1[,3],method="wc",eta=0.5,cv2)


# test with psi2
test.once.psi(m,psi2[,3],method="ps",eta=0.45,cv1)

test.once.psi(m,psi2[,3],method="wc",eta=0.5,cv2)