factor.seg.alg: Simultaneous multiple change-point and factor analysis for...
In factorcpt: Simultaneous Change-Point and Factor Analysis

Description Usage Arguments Value Author(s) References Examples

The function applies the two-stage methodology for multiple change-point detection under factor modelling. It first transforms the input time series into panels of statistics that contain the change-points in the second-order structure of the common and idiosyncratic components, as change-points in their ‘means’, to which the Double CUSUM Binary Segmentation algorithm is applied in the second stage. The function returns change-point estimates from the common and idiosyncratic components separately.

factor.seg.alg(x, r=NULL, bn.op=2, sig.lev=.05, max.q=NULL, q.seq=NULL,
              qlen=5, qby=0, dw=NULL, p=NULL, B=200, scales=NULL,
              rule=NULL, mby=NULL, tby=NULL, idio.diag=FALSE,
              do.parallel=TRUE, no.proc=2)

`x`	input time series matrix, with each row representing a time series
`r`	the number of factors, if `r=NULL`, screening over a range of factor number candidates is performed as described in the paper
`bn.op`	an index number for the information criterion-based estimator of Bai and Ng (2002) for the number of factors, the default value `bn.op=2` is used in Barigozzi, Cho & Fryzlewicz (2016)
`sig.lev`	sets the level of significance for drawing the bootstrap-based threshold
`max.q`	the maximum number of factors, if `max.q=NULL`, a default value is chosen as described in the paper
`q.seq`	a vector of factor number candidates; if `q.seq=NULL`, it is chosen as described in Barigozzi, Cho & Fryzlewicz (2016) using `qlen` or `qby`
`qlen`	specifies the length of the sequence of factor number candidates
`qby`	specifies the increment of the sequence of factor number candidates when `qlen=0`; if both `qlen=0` and `qby=0`, the sequence of factor number candidates is generated as if `qby=1`
`dw`	trims off the interval of consideration in the binary segmentation algorithm and determines the minimum length of a stationary segment; if `dw=NULL`, a default value is chosen as described in the Appendix of Barigozzi, Cho & Fryzlewicz (2016)
`p`	inverse of the average length of blocks in the stationary bootstrap procedure, if `p=NULL`, a data-driven value is chosen as described in the Appendix of Barigozzi, Cho & Fryzlewicz (2016)
`B`	the number of bootstrap samples for threshold selection
`scales`	the number of wavelet scales used for wavelet filtering of the common and idiosyncratic components estimated via PCA
`rule`	the depth of a binary tree for change-point analysis, see the Appendix of Barigozzi, Cho & Fryzlewicz (2016)
`mby`	see `dmby` in `func_dc_by`
`tby`	see `dtby` in `func_dc_by`
`idio.diag`	if `idio.diag=TRUE`, only the diagonal wavelet-transform is employed in order to generate the panel of statistics from the idiosyncratic components
`do.parallel`	if `do.parallel=TRUE`, a set of copies of R running in parallel are created and used for bootstrap procedure
`no.proc`	sets the number of processes to be spawned when `do.parallel=TRUE`,

`cs.list`	a list of objects returned by an internal function `common.seg`, which contain the results from performing change-point analysis on the common components estimated with a range of factor number candidates
`r`	the factor number selected from performing change-point analysis on the common component
`common.est.cps`	change-points detected from the common component estimated with `r` as the factor number
`idio.seg.res`	an object returned by an internal function `idio.seg`, which contains the results from performing change-point analysis on the idiosyncratic component estimated with `r` as the factor number
`idio.est.cps`	change-points detected from the idiosyncratic component
`gfm`	factor structure of `x` estimated from `get.factor.model`
`q.seq`	a vector containing the range of factor number candidates

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.

H. Cho (2016) Change-point detection in panel data via double CUSUM statistic. Electronic Journal of Statistics. 10: 2000-2038.

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[, 1:chp] <- Lam%*%f[, 1:chp]
Lam <- Lam + matrix(rnorm(n*r, 0, sqrt(2)), nrow=n) # new loadings
chi[, (chp+1):T] <- Lam%*%f[, (chp+1):T]
x <- chi + sqrt(r)*e

fsa <- factor.seg.alg(x, idio.diag=TRUE)
fsa$common.est.cps
fsa$idio.est.cps
fsa$q.seq