Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading

By Ole E. Barndorff-Nielsen, P. R. Hansen, Asger Lunde, N. Shephard. 2011

606 citations recorded by the source corpus.

We propose a multivariate realised kernel to estimate the ex-post covariation of log-prices. We show this new consistent estimator is guaranteed to be positive semi-definite and is robust to measurement noise of certain types and can also handle non-synchronous trading. It is the first estimator which has these three properties which are all essential for empirical work in this area. We derive the large sample asymptotics of this estimator and assess its accuracy using a Monte Carlo study. We implement the estimator on some US equity data, comparing our results to previous work which has used returns measured over 5 or 10 minutes intervals. We show the new estimator is substantially more precise.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/7518c48650482602415fa3031c401c016dcd36d7

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Citations in the corpus

Estimation of integrated volatility of volatility with applications to goodness-of-fit testing (2011, background): “See, for example, [6] for a thorough discussion in a general multivariate setting.”
MGARCH models: Trade-off between feasibility and flexibility (2018, methodology): “…into 288 five-minute intervals9 to avoid the asynchronous effect and compute the realized covariance by the Realized Outlyingness Weighted Covariance (rOWCov) of Boudt et al. (2011)10; see Barndorff-Nielsen et al. (2011), Corsi and Audrino (2012) and Boudt et al. (2012) for alternative proxies.”
Irregular sampling and central limit theorems for power variations: The continuous case (2011, background): “is relatively close to the present paper, and [6–9] and [2] when the process is multidimensional and the observation times exhibit some sort of relatively restricted randomness, or are random but independent of the observed process.”
Asymmetric Connectedness on the U.S. Stock Market: Bad and Good Volatility Spillovers (2015, positive): “Due to the work of Barndorff-Nielsen et al. (2010), we can conveniently decompose daily volatility into negative (and positive) semivariance, providing a proxy for downside (and upside) risk. Replacing the total volatility, which enters the computation by the measures of downside (upside) risk, will”
Econometric Analysis of Vast Covariance Matrices Using Composite Realized Kernels and Their Application to Portfolio Choice (2016, background): “The implications 1For details about jittering, see Barndorff-Nielsen et al. (2011). of alternative choices for k were discussed by Barndorff-Nielsen et al. (2008, 2011), although these are not of core importance here.”
Vast Portfolio Selection with Gross-exposure Constraints (2012, neutral): “One can also aggregate the large covariance matrix estimation based on the high-frequency data (Barndorff-Nielsen and Shephard 2002; Zhang, Mykland, and Aı̈t-Sahalia 2005; Barndorff-Nielsen et al. 2011).”
Statistical Properties of Microstructure Noise (2013, neutral): “For example, the two-scale method as in Zhang et al. (2005), Aït-Sahalia et al. (2005); the kernel method as in Barndorff-Nielsen et al. (2008), Barndorff-Nielsen et al. (2011); the pre-averaging method as in Jacod et al. (2009), Kinnebrock et al. (2010); the multi-scale method as in Zhang (2006);…”
Realized Wishart-Garch: A Score-Driven Multi-Asset Volatility Model (2016, positive): “In the case of multiple assets, realized measures of asset covariance have also been proposed and considered; see Christensen, Kinnebrock, and Podolskij (2010), Barndorff-Nielsen et al. (2011a), Griffin and Oomen (2011), and references therein.”
Modeling Realized Covariances and Returns (2013, methodology): “(10) Wishartk(ν, St−1) denotes a Wishart distribution over positive definite matrices of dimension k with ν > k−1 degrees of freedom and scale matrix St−1.”