Nonparametric threshold estimation of spot volatility based on high-frequency data for time-dependent diffusion models with jumps

We construct a spot volatility kernel estimator of time-dependent diffusion models with jumps. Instead of idiomatic intraday return over an observation interval, in the proposed estimator, we use intraday range. Since the range represents the maximum difference among all observations within an interval, all data are used, and no information is lost. By setting a reasonable threshold and making the range not greater than it we effectively eliminate the negative effect of jump on volatility estimation. In this paper, we also prove the consistency and asymptotic normality of the estimator and testify its higher accuracy.