We develop a new efficient and analytically tractable method for estimation of parametric volatility models that is robust to price-level jumps and generally has good finite sample properties. The method entails first integrating intra-day data into the Realized Laplace Transform of volatility, which is a model-free and jump-robust estimate of daily integrated empirical Laplace transform of the...

There is an emerging consensus in empirical finance that realized volatility series typically display long range dependence with a memory parameter (d) around 0.4 (Andersen et. al. (2001), Martens et. al. (2004)). The present paper provides some analytical explanations for this evidence and shows how recent results in Lieberman and Phillips (2004a, 2004b) can be used to refine statistical infer...

We propose flexible models for multivariate realized volatility dynamics which involve generalizations of the Box-Cox transform to the matrix case. The matrix Box-Cox model of realized covariances (MBC-RCov) is based on transformations of the covariance matrix eigenvalues, while for the Box-Cox dynamic correlation (BC-DC) specification the variances are transformed individually and modeled join...

This paper shows that the asymptotic normal approximation is often insufficiently accurate for volatility estimators based on high frequency data. To remedy this, we compute Edgeworth expansions for such estimators. Unlike the usual expansions, we have found that in order to obtain meaningful terms, one needs to let the size of the noise to go zero asymptotically. The results have application t...

Financial series such as stock returns follow a different generating process from the relevant economic series. The key different between each other is that financial time series have some key features which cannot be captured by models such as ARMA. ARMA, which is referred as autoregressive moving-average, models consist a good approximation for economic series but not for financial series. In...

This paper discusses the effects of extended hours trading, i.e. trading that occurs between market close at 16:00 and reopen the next business day at 09:30, on models of daytime realized volatility. Focusing on the impact of data enrichment, rather than model specification, the in-sample and out-of-sample effects are demonstrated in the context of an AR(1) model. The model is estimated using 2...

When estimating integrated volatilities based on high-frequency data, simplifying assumptions are usually imposed on the relationship between the observation times and the price process. In this paper, we establish a central limit theorem for the Realized Volatility in a general endogenous time setting. We ∗We are grateful to Andrew Patton and Neil Shephard, and the participants of the Stevanov...