Lack of Fit Test for Infinite Variation Jumps at High Frequencies

Abstract

In this paper, we are concerned with testing for infinite variation jumps in addition to a continuous local martingale component driven by Brownian motion using high-frequency data. We developed a lack of fit type test based on the empirical distribution of the devolatized increments. Under the null that the jump component is of finite variation, the empirical process associated with the devolatized increments converges to a Gaussian process in the Skorohod topology. Under the alternative hypothesis that the jumps are of infinite variation, that empirical process explodes instead. Theoretical results show good performance of the size and power. Simulation studies justify the theory. A real financial data set is analyzed.