get.factor.model: Factor model estimation via Principal Component Analysis
In factorcpt: Simultaneous Change-Point and Factor Analysis

Description Usage Arguments Value Author(s) References Examples

Estimates the components of the factor structure for an input time series, such as loadings and factors, as well as estimating the number of factors.

1 2	get.factor.model(x, max.q = NULL, q = NULL, bn = TRUE, bn.op = 2, normalisation = TRUE)

`x`	input time series matrix, with each row representing a time series
`max.q`	see `max.q` in `factor.seg.alg`
`q`	the number of factors; if `bn=FALSE`, `q` needs to be given
`bn`	if `bn=TRUE`, the factor number is estimated using the information criterion-based estimator of Bai and Ng (2002)
`bn.op`	an index number for the information criterion-based estimator of Bai and Ng (2002); the default value `bn.op=2` is used in Barigozzi, Cho & Fryzlewicz (2016)
`normalisation`	if `normalisation=TRUE`, each row `x` is standardised prior to PCA

`lam`	an `n`-by-`(min(n, T)-1)` matrix containing the estimated loadings
`f`	a `(min(n, T)-1)`-by-`T` matrix containing the estimated factors
`norm.x`	if `normalisation=TRUE`, row-wise standardised `x`; else `norm.x=x`
`q.hat`	estimated number of factors
`max.q`	the maximum factor number used for factor number estimation
`ic`	information criterion values computed at a range of factor numbers from `0` to `max.q`

Haeran Cho

J. Bai and S. Ng (2002) Determining the number of factors in approximate factor models. Econometrica. 70: 191-221.

M. Barigozzi, H. Cho and P. Fryzlewicz (2016) Simultaneous multiple change-point and factor analysis for high-dimensional time series, Preprint.

n <- 50; T <- 200
e <- matrix(rnorm(n*T), nrow=n) # idiosyncratic components
r <- 3 # factor number
Lam <- matrix(rnorm(n*r, 1, 1), nrow=n) # loadings
f <- matrix(rnorm(r*T), nrow=r) # factors
chi <- e*0 # common component
chp <- T/2 # change-point
chi <- Lam%*%f
x <- chi + sqrt(r)*e

gfm <- get.factor.model(x)
gfm$q.hat