OLCPM (version 0.1.1)

KSTP: 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
)

Value

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

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)

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)))