  Estimating spot covariance is an important issue to study, especially with
the increasing availability of high-frequency financial data. We study the
estimation of spot covariance using a kernel method for high-frequency data. In
particular, we consider first the kernel weighted version of realized
covariance estimator for the price process governed by a continuous
multivariate semimartingale. Next, we extend it to the threshold kernel
estimator of the spot covariances when the underlying price process is a
discontinuous multivariate semimartingale with finite activity jumps. We derive
the asymptotic distribution of the estimators for both fixed and shrinking
bandwidth. The estimator in a setting with jumps has the same rate of
convergence as the estimator for diffusion processes without jumps. A
simulation study examines the finite sample properties of the estimators. In
addition, we study an application of the estimator in the context of covariance
forecasting. We discover that the forecasting model with our estimator
outperforms a benchmark model in the literature.
