Rank Tests at Jump Events

Jia Li*, Viktor Todorov, George Tauchen, Huidi Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)312-321
Number of pages10
JournalJournal of Business and Economic Statistics
Issue number2
StatePublished - Apr 3 2019


  • Factor model
  • High-frequency data
  • Jumps
  • Rank test
  • Semimartingale

ASJC Scopus subject areas

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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