Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2020 025

Non-Parametric Estimation of Spot Covariance Matrix with High-Frequency Data

Konul Mustafayeva
Weining Wang

Estimating spot covariance is an important issue to study, especially with the
increasing availability of high-frequency nancial data. We study the estimation
of spot covariance using a kernel method for high-frequency data. In particular,
we consider rst 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 nite activity jumps. We derive the asymptotic distribution of the
estimators for both xed and shrinking bandwidth. The estimator in a setting
with jumps has the same rate of convergence as the estimator for di usion
processes without jumps. A simulation study examines the nite 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.

high-frequency data; kernel estimation; jump; forecasting covariance matrix

JEL Classification: