Simultaneous multiple change-point and factor analysis for high-dimensional time series
提出首个综合处理高维时间序列因子模型中二阶结构多变点的方法，能一致估计变点数量和位置并识别其来源，通过小波变换将问题转化为高维面板数据均值变点检测，并采用筛选程序避免准确估计因子数。
We propose the first comprehensive treatment of high-dimensional time series\nfactor models with multiple change-points in their second-order structure. We\noperate under the most flexible definition of piecewise stationarity, and\nestimate the number and locations of change-points consistently as well as\nidentifying whether they originate in the common or idiosyncratic components.\nThrough the use of wavelets, we transform the problem of change-point detection\nin the second-order structure of a high-dimensional time series, into the\n(relatively easier) problem of change-point detection in the means of\nhigh-dimensional panel data. Also, our methodology circumvents the difficult\nissue of the accurate estimation of the true number of factors in the presence\nof multiple change-points by adopting a screening procedure. We further show\nthat consistent factor analysis is achieved over each segment defined by the\nchange-points estimated by the proposed methodology. In extensive simulation\nstudies, we observe that factor analysis prior to change-point detection\nimproves the detectability of change-points, and identify and describe an\ninteresting `spillover' effect in which substantial breaks in the idiosyncratic\ncomponents get, naturally enough, identified as change-points in the common\ncomponents, which prompts us to regard the corresponding change-points as also\nacting as a form of `factors'. Our methodology is implemented in the R package\n{\\tt factorcpt}, available from CRAN.\n