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

## TL;DR

This paper introduces a kernel-based method for estimating the instantaneous covariance matrix of high-frequency financial data, effectively handling both continuous and jump processes, with proven asymptotic properties and practical forecasting improvements.

## Contribution

It develops a novel kernel and threshold kernel estimator for spot covariance that accounts for jumps, with established asymptotic distributions and superior forecasting performance.

## Key findings

- Estimator has the same convergence rate with and without jumps.
- Simulation confirms good finite sample properties.
- Forecasting model with the new estimator outperforms benchmarks.

## Abstract

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.