Rank Tests at Jump Events
提出一种检验跳跃事件时刻截面过程秩的方法，通过阈值估计跳跃事件并计算特征值，用重抽样实现可行检验。应用于2007-2015年股市跳跃数据，发现市场跳跃时股票收益呈单因子结构，与正常时期的高维因子结构不同。
We propose a test for the rank of a cross-section of processes at a set of jump events. The jump events are either specific known times or are random and associated with jumps of some process. The test is formed from discretely sampled data on a fixed time interval with asymptotically shrinking mesh. In the first step, we form nonparametric estimates of the jump events via thresholding techniques. We then compute the eigenvalues of the outer product of the cross-section of increments at the identified jump events. The test for rank r is based on the asymptotic behavior of the sum of the squared eigenvalues excluding the largest r. A simple resampling method is proposed for feasible testing. The test is applied to financial data spanning the period 2007–2015 at the times of stock market jumps. We find support for a one-factor model of both industry portfolio and Dow 30 stock returns at market jump times. This stands in contrast with earlier evidence for higher-dimensional factor structure of stock returns during “normal” (nonjump) times. We identify the latent factor driving the stocks and portfolios as the size of the market jump.