Abstract
In this paper, we consider the problem of (multiple) change-point detection in panel data. We propose the double CUSUM statistic which utilises the cross-sectional change-point structure by examining the cumulative sums of ordered CUSUMs at each point. The efficiency of the proposed change-point test is studied, which is reflected on the rate at which the cross-sectional size of a change is permitted to converge to zero while it is still detectable. Also, the consistency of the proposed change-point detection procedure based on the binary segmentation algorithm, is established in terms of both the total number and locations (in time) of the estimated change-points. Motivated by the representation properties of the Generalised Dynamic Factor Model, we propose a bootstrap procedure for test criterion selection, which accounts for both cross-sectional and within-series correlations in high-dimensional data. The empirical performance of the double CUSUM statistics, equipped with the proposed bootstrap scheme, is investigated in a comparative simulation study with the state-of-the-art. As an application, we analyse the log returns of S&P 100 component stock prices over a period of one year.
Highlights
Multivariate, possibly high-dimensional observations over time have emerged in many fields, such as economics, finance, natural science, engineering and humanities, thanks to the advances of computing technologies (Fan, Lv and Qi, 2011)
T Jirak appears to be highly sensitive and vulnerable to the choice of σj when the critical value is selected by the parametric bootstrap, since the test statistic directly depends on the largest CUSUM value attained by a single component series
We have proposed the double CUSUM (DC) statistic, a novel way of aggregating high-dimensional CUSUM series across the panel for change-point analysis, and showed its consistency in single and multiple change-point detection both theoretically and empirically
Summary
Multivariate, possibly high-dimensional observations over time have emerged in many fields, such as economics, finance, natural science, engineering and humanities, thanks to the advances of computing technologies (Fan, Lv and Qi, 2011). We focus on the problem of detecting (possibly) multiple change-points in the mean of panel data, where n, the dimensionality of the data, may increase with the number of observations T. For segmenting n-dimensional panel data, we may apply the above procedure to each univariate component series separately, and prune down the estimated change-points by identifying those detected for the identical changepoint across the panel. Such pruning may be difficult to accomplish even in moderately large dimensions, due to the estimation bias present in each change-point estimate. We propose to segment the n-dimensional data simultaneously by searching for change-points from the aggregation of n series of CUSUM statistics, rather than from individual CUSUM series separately
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
