Estimating the Spot Covariation of Asset Prices - Statistical Theory and Empirical Evidence

TL;DR

This paper introduces a new statistical estimator for the instantaneous covariance of asset prices, accounting for noise and asynchronous data, with theoretical validation and empirical application to high-frequency stock data.

Contribution

It develops a novel local spectral covariance estimator based on the local method of moments, extending it to handle autocorrelated noise and providing theoretical guarantees.

Findings

Estimator performs well in simulations and real data.

Intraday covariances exhibit periodicity and variability.

Covariance can spike with new information.

Abstract

We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semi-martingale log asset price process which is subject to noise and non-synchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance estimates. The latter originate from a local method of moments (LMM) which recently has been introduced. We prove consistency and a point-wise stable central limit theorem for the proposed spot covariance estimator in a very general setup with stochastic volatility, leverage effects and general noise distributions. Moreover, we extend the LMM estimator to be robust against autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. Based on simulations we provide empirical guidance on the effective implementation of the estimator and apply it to high-frequency data of a cross-section of Nasdaq blue chip stocks. Employing the estimator to estimate spot covariances, correlations and volatilities in normal but also unusual periods yields novel insights into intraday covariance and correlation dynamics. We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, and (iii) can increase strongly and nearly instantaneously if new information arrives.