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

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 {\tt factorcpt}, available from CRAN.

64 pages, to appear in the Journal of Econometrics

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Cited by in corpus (16)

• Selective review of offline change point detection methods
• Finite sample change point inference and identification for high-dimensional mean vectors
• Recent Developments on Factor Models and its Applications in Econometric Learning
• Sequential testing for structural stability in approximate factor models
• Change Point Detection for Nonparametric Regression under Strongly Mixing Process
• Data segmentation algorithms: Univariate mean change and beyond
• A review on minimax rates in change point detection and localisation
• Consistent estimation of high-dimensional factor models when the factor number is over-estimated
• Change Point Estimation in Panel Data with Temporal and Cross-sectional Dependence
• Change-point detection using spectral PCA for multivariate time series
• Spectral Change Point Estimation for High Dimensional Time Series by Sparse Tensor Decomposition
• Network-Assisted Estimation for Large-dimensional Factor Model with Guaranteed Convergence Rate Improvement
• High-dimensional GARCH process segmentation with an application to Value-at-Risk
• Subspace Change-Point Detection via Low-Rank Matrix Factorisation
• Ultra High Dimensional Change Point Detection
• Factor Analysis for High-Dimensional Time Series with Change Point