Jump Variation in High-Frequency Asset Returns: New Estimation Methods

Abstract

A large literature has emerged in the last 10 years using high-frequency (intraday) asset returns to estimate lower-frequency phenomena, several of which being conditional daily return variance and its components jump variation and integrated variance. We propose several new estimators of jump variation and integrated variance. We base the first set on the jump detection work of Lee and Mykland (2008). Simply, these estimate jump variation by summing the hard-thresholded or naively shrunk squared returns (and estimate integrated variance as the residual of realized variance). In the second set, we appeal to Johnstone and Silverman (2004, 2005) for their discrete Bayesian model of a sparse signal plus noise and argue for its use as a model of high-frequency asset returns with jumps. Within this model, we derive optimal estimators of jump variation and integrated variance. In a simulation analysis, we find outperformance of our estimators against the established. In an empirical analysis we find dramatically different estimates of jump variation and integrated variance based on the estimation scheme, suggesting careful attention must be paid to the method of decomposing conditional daily return variance into jump variation and integrated variance.