  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.
