IQR {HDRFA}

Iterative Quantile Regression Methods for Quantile Factor Models

Description

This function is to fit the quantile factor model via the Iterative Quantile Regression (IQR) algorithm.

Usage

IQR(X, r, tau, L_init = NULL, F_init = NULL, max_iter = 100, eps = 0.001)

Arguments

X

Input matrix, of dimension T\times N. Each row is an observation with N features at time point t.

r

A positive integer indicating the factor numbers.

tau

The user-supplied quantile level.

L_init

User-supplied inital value of loadings; default is the PCA estimator.

F_init

User-supplied inital value of factors; default is the PCA estimator.

max_iter

The maximum number of iterations. The default is 100.

eps

The stopping critetion parameter. The default is 1e-06.

Details

See Chen et al. (2021) and He et al. (2023) for details.

Value

The return value is a list. In this list, it contains the following:

Fhat

The estimated factor matrix of dimension T\times r.

Lhat

The estimated loading matrix of dimension N\times r.

t

The number of iterations.

Author(s)

Yong He, Lingxiao Li, Dong Liu, Wenxin Zhou.

References

Chen, L., Dolado, J.J., Gonzalo, J., 2021. Quantile factor models. Econometrica 89, 875–910.

He Y, Kong X, Yu L, Zhao P., 2023 Quantile factor analysis for large-dimensional time series with statistical guarantee <arXiv:2006.08214>.

Examples

set.seed(1)
T=50;N=50;r=3
L=matrix(rnorm(N*r,0,1),N,r);F=matrix(rnorm(T*r,0,1),T,r)
E=matrix(rnorm(T*N,0,1),T,N)
X=F%*%t(L)+E

tau=0.5
fit=IQR(X,r,tau)
fit$Fhat;fit$Lhat