F_FASeg {FASeg}

Joint Segmentation of Set of Correlated Time-Series

Description

This function is dedicated to the joint segmentation (the segmentation is series-specific) in the mean of several correlated series. The form of the correlation is assumed to be arbitrary and we propose to model it with a factor model. A EM algorithm is used to estimate the parameters. A model selection procedure is also proposed to determine both the number of breakpoints and the number of factors.

Usage

F_FASeg(Y, uniKmax, multiKmax, qmax, selection, WithoutCorr)

Arguments

Y

Data frame, with size [(n*M) x 3], which contains the data and other informations, n is the length of each series and M is the number of series

uniKmax

Maximal number of segments per series (uniKmax will be lower or equal to n)

multiKmax

Maximal number of segments for all the series (multiKmax will be greater or equal to M)

qmax

Maximal number of factors (qmax will be lower or equal to M-1) (default qmax=M-1). If qmax=0 then a joint segmentation with multiKmax segments and without taking into account the correlation between series is performed

selection

A logical value indicating if the selection of the number of segments K and the number of factors Q is performed (default=TRUE). If it is TRUE, K and Q are selected; if it is FALSE, K is fixed to multiKmax and Q is fixed to qmax

WithoutCorr

A logical value indicating if, when K and Q are selected, the joint segmentation without taking into account the correlation between series is also a possible solution in the selection (default=FALSE)

Value

Contains the following attributes:

SelectedK

Selected number of segments for all the series if selection=TRUE, the number of segments fixed by the user otherwise (K=multiKmax)

Selectedq

Selected number of factors if selection=TRUE, the number of factors fixed by the user otherwise (Q=qmax)

SelectedSigma

Estimation of the covariance matrix Sigma

SelectedPsi

Estimation of the matrix Psi

SelectedB

Estimation of the matrix of coefficients B

SelectedZ

Estimation of the latent vectors Z

SelectedSeg

Optimal segmentation with a selected or fixed value of the number of segments and the number of factors

Author(s)

Xavier Collilieux, Emilie Lebarbier and Stephane Robin

References

A factor model approach for the joint segmentation with between-series correlation (arXiv:1505.05660)