This paper analyses multivariate high frequency financial data using realized covariation. We provide a new asymptotic distribution theory for standard methods such as regression, correlation analysis, and covariance. It will be based on a fixed interval of time (e.g., a day or week), allowing the number of high frequency returns during this period to go to infinity. Our analysis allows us to study how high frequency correlations, regressions, and covariances change through time. In particular we provide confidence intervals for each of these quantities.

This paper is concerned with the Bayesian estimation of nonlinear stochastic differential equations when observations are discretely sampled. The estimation framework relies on the introduction of latent auxiliary data to complete the missing diffusion between each pair of measurements. Tuned Markov chain Monte Carlo (MCMC) methods based on the Metropolis-Hastings algorithm, in conjunction with the Euler-Maruyama discretization scheme, are used to sample the posterior distribution of the latent data and the model parameters. Techniques for computing the likelihood function, the marginal likelihood, and diagnostic measures (all based on the MCMC output) are developed. Examples using simulated and real data are presented and discussed in detail.

GARCH models are commonly used as latent processes in econometrics, financial economics, and macroeconomics. Yet no exact likelihood analysis of these models has been provided so far. In this paper we outline the issues and suggest a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a Bayesian solution in O(T) computational operations, where T denotes the sample size. We assess the performance of our proposed algorithm in the context of both artificial examples and an empirical application to 26 UK sectorial stock returns, and compare it to existing approximate solutions.

This paper shows how to use realized kernels to carry out efficient feasible inference on the ex post variation of underlying equity prices in the presence of simple models of market frictions. The weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which equals that of the maximum likelihood estimator in the parametric version of this problem. Realized kernels can also be selected to (i) be analyzed using endogenously spaced data such as that in data bases on transactions, (ii) allow for market frictions which are endogenous, and (iii) allow for temporally dependent noise. The finite sample performance of our estimators is studied using simulation, while empirical work illustrates their use in practice. Copyright 2008 The Econometric Society.