# Simultaneous multiple change-point and factor analysis for high-dimensional time series

*Matteo Barigozzi*,
*Haeran Cho* and
*Piotr Fryzlewicz*

*Journal of Econometrics*, 2018, vol. 206, issue 1, 187-225

**Abstract:**
We propose the first comprehensive treatment of high-dimensional time series factor models with multiple change-points in their second-order structure. We operate under the most flexible definition of piecewise stationarity, and estimate the number and locations of change-points consistently as well as identifying whether they originate in the common or idiosyncratic components. Through the use of wavelets, we transform the problem of change-point detection in the second-order structure of a high-dimensional time series, into the (relatively easier) problem of change-point detection in the means of high-dimensional panel data. Also, our methodology circumvents the difficult issue of the accurate estimation of the true number of factors in the presence of multiple change-points by adopting a screening procedure. We further show that consistent factor analysis is achieved over each segment defined by the change-points estimated by the proposed methodology. In extensive simulation studies, we observe that factor analysis prior to change-point detection improves the detectability of change-points, and identify and describe an interesting ‘spillover’ effect in which substantial breaks in the idiosyncratic components get, naturally enough, identified as change-points in the common components, which prompts us to regard the corresponding change-points as also acting as a form of ‘factors’. Our methodology is implemented in the R package factorcpt, available from CRAN.

**Keywords:** Piecewise stationary factor model; Change-point detection; Principal component analysis; Wavelet transformation; Double CUSUM binary segmentation (search for similar items in EconPapers)

**Date:** 2018

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Working Paper: Simultaneous multiple change-point and factor analysis for high-dimensional time series (2018)

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:econom:v:206:y:2018:i:1:p:187-225

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