POETKhat {POET}

Khat - number of factors in approximate factor model

Description

This function is for calculating the optimal number of factors in an approximate factor model.

Usage

POETKhat(Y)

Arguments

Y

p by n matrix of raw data, where p is the dimensionality, n is the sample size. It is recommended that Y is de-meaned, i.e., each row has zero mean.

Details

This method was proposed by Bai & Ng (2002) and Hallin & Liska (2007). They propose two penalty functions and in turn minimize the corresponding information criteria. Notice that this method may underestimate K. POET is very robust to over-estimating K. But under-estimating K can result to VERY BAD performance. Therefore we strongly recommend choosing a relatively large K (normally less than 8) to avoid missing any important common factor.

Value

K1HL

estimated number of factors based on the first infomation criterion using Hallin & Liska method

K2HL

estimated number of factors based on the second information criterion using Hallin & Liska method

K1BN

estimated number of factors based on the first infomation criterion using Bai & Ng method

K2BN

estimated number of factors based on the second information criterion using Bai & Ng method

Author(s)

Jianqing Fan, Yuan Liao, Martina Mincheva

References

Bai,Ng,2002.Determining the number of factors in approximate factor models. Econometrica 70,191-221.

Hallin,Liska,2007.Determining the number of factors in the general dynamic factor model.JASA 102,603-617.

Alessi,Barigozzi,Capasso,2010. Improved penalization for determining the number of factors in approximate factor models. Statistics and Probability Letters 80, 1806-1813.

Examples

p=100
n=100
Y<-array(rnorm(p*n),dim=c(p,n))
K<-POETKhat(Y)