Jumps, Jump Regression, and Rank Tests at Jump Events
The presentation provides an overview of recent research on jump discontinuities in financial time series. Specific topics include jump detection, jump regression, and the covariance structure of equity returns at times of market jumps. The presentation includes a heuristic review of the asymptotic theory for statistical inference in the jump setting along with techniques for estimation and inference about the covariation structure equity returns at times of financial stress. More detail is provided on a test rank on of the rank of the covariance matrix of a cross-section of stock returns at a set of jump events. The test is formed from discretely sampled data on a fixed time interval with asymptotically shrinking mesh. To implement the test, one computes 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. There is strong empirical support for a one factor model of both sector portfolios and Dow 30 stock returns at market jump times. This finding stands in sharp contrast to extensive evidence for a 3-5 dimensional factor structure of stock returns during ordinary (non-jump) times.
Dr Chau Chak Wing Building
