factorcpt (version 0.1.2)

post.cpts.analysis: Display the results from change-point analysis and factor modelling

Description

Computes the minimum number of eigenvalues required so that the given proportion of the variance of x over each segment, defined by the change-points detected from the common components, by varying the proportion and plots the number of eigenvalues.

Usage

post.cpts.analysis(x, est.cps, cutoff.seq = seq(0.5, 0.95, by = 0.05), do.plot = TRUE)

Arguments

x

input time series

est.cps

a vector containing the change-points estimated for the common components

cutoff.seq

a sequence containing the proportions between zero and one

do.plot

if do.plot=TRUE, produces a plot of minimum numbers of eigenvalues required for accounting for the given proportion of variance, over time (x-axis) and the level of proportion (y-axis).

Value

a matrix containing the minimum numbers of eigenvalues for varying levels of proportions over the segments defined by two neighbouring change-points in the common components

References

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

Examples

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

post.cpts.analysis(x, 100)