An efficient estimator is constructed for the quadratic covariation or integrated co-volatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under high-frequency asymptotics. Our approach relies on an asymptotically equivalent continuous-time observation model where a local generalised method of moments in the spectral domain turns out to be optimal. Asymptotic semi-parametric efficiency is established in the Cramér-Rao sense. Main findings are that nonsynchronicity of observation times has no impact on the asymptotics and that major efficiency gains are possible under correlation. Simulations illustrate the finite-sample behaviour.

This paper addresses the open debate about the usefulness of high-frequency (HF) data in large-scale portfolio allocation. We consider the problem of constructing global minimum variance portfolios based on the constituents of the S&P 500 over a four-year period covering the 2008 financial crisis. HF-based covariance matrix predictions are obtained by applying a blocked realized kernel estimator, different smoothing windows, various regularization methods and two forecasting models. We show that HF-based predictions yield a significantly lower portfolio volatility than methods employing daily returns. Particularly during the volatile crisis period, these performance gains hold over longer horizons than previous studies have shown and translate into substantial utility gains from the perspective * For helpful comments and discussions we thank Frank Diebold and three anonymous referees, Bent Jesper

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SummaryThis paper addresses the debate about the usefulness of high‐frequency (HF) data in large‐scale portfolio allocation. We construct global minimum variance portfolios based on the constituents of the S&P 500. HF‐based covariance matrix predictions are obtained by applying a blocked realized kernel estimator, different smoothing windows, various regularization methods and two forecasting models. We show that HF‐based predictions yield a significantly lower portfolio volatility than methods employing daily returns. Particularly during the 2008 financial crisis, these performance gains hold over longer horizons than previous studies have shown, translating into substantial utility gains for an investor with pronounced risk aversion. Copyright © 2013 John Wiley & Sons, Ltd.

Standard fixed symmetric kernel type density estimators are known to encounter problems for positive random variables with a large probability mass close to zero. We show that in such settings, alternatives of asymmetric gamma kernel estimators are superior but also differ in asymptotic and finite sample performance conditional on the shape of the density near zero and the exact form of the chosen kernel. We therefore suggest a refined version of the gamma kernel with an additional tuning parameter according to the shape of the density close to the boundary. We also provide a data-driven method for the appropriate choice of the modified gamma kernel estimator. In an extensive simulation study we compare the performance of this refined estimator to standard gamma kernel estimates and standard boundary corrected and adjusted fixed kernels. We find that the finite sample performance of the proposed new estimator is superior in all settings. Two empirical applications based on high-frequency stock trading volumes and realized volatility forecasts demonstrate the usefulness of the proposed methodology in practice.