KSTP {OLCPM}

determine row factor number - test

Description

This function determines the number of row factors under a two-way factor structure, using randomized test method.

Usage

KSTP(
  Y,
  alpha = 0.05,
  type = "proj",
  kmax = 4,
  epsilon = 0.05,
  r = 8,
  M = 100,
  S = 100,
  fq = 1/4
)

Arguments

Y

data, a T\times p1\times p2 array.

alpha

a number in (0,1), indicating the significance of the test.

type

indicates how to calculate the sample covariance. "flat" for the flat version, while others for the projected version.

kmax

a positive integer smaller than p2, indicating the upper bound for the factor numbers, and the dimension of projection matrix.

epsilon

a small positive number in (0,1), indicating the size of scaling.

r

a positive number indicating the order of the power function for transforming the rescaled eigenvalue.

M

a large integer for the number of Gaussian variables in the randomized test.

S

another large integer for the number of replications in the strong rule. Usually M=S=T.

fq

a number in (0,0.5), controlling the threshold function of the strong rule.

Details

See He et al. (2023)

Value

an integer for the number of row factors. To determine the number of column factors, just transpose the observation matrices.

References

He Y, Kong X, Trapani L, & Yu L (2023). One-way or two-way factor model for matrix sequences? Journal of Econometrics, 235(2), 1981-2004.

Examples

k1=3
k2=3
Sample_T=100
p1=40
p2=20

Y=gen.data(Sample_T,p1,p2,k1,k2,tau=0.5,change=0)
KSTP(Y)
KSTP(aperm(Y,c(1,3,2)))