We develop econometric tools for studying jump dependence of two processes from high-frequency observations on a fixed time interval. In this context, only segments of data around a few outlying observations are informative for the inference. We derive an asymptotically valid test for stability of a linear jump relation over regions of the jump size domain. The test has power against general forms of nonlinearity in the jump dependence as well as temporal instabilities. We further propose an optimal estimator for the linear jump regression model that is formed by optimally weighting the detected jumps with weights based on the diffusive volatility around the jump times. We derive the asymptotic limit of the estimator, a semiparametric lower efficiency bound for the linear jump regression, and show that our estimator attains the latter. The analysis covers both deterministic and random jump arrivals. A higher-order asymptotic expansion for the optimal estimator further allows for finite-sample refinements. In an empirical application, we use the developed inference techniques to test the stability (in time and jump size) of market jump betas.
|Original language||English (US)|
|Number of pages||54|
|State||Published - Nov 23 2015|