This paper proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time series models. The model is parametric and quite general, and, in particular, encompasses the...

We introduce the Realized Exponential GARCH model that can utilize multiple realized volatility measures for the modeling of a return series. The model specifies the dynamic properties of both returns and realized measures, and is characterized by a flexible modeling of the dependence between...

We introduce a multivariate estimator of financial volatility that is based on the theory of Markov chains. The Markov chain framework takes advantage of the discreteness of high-frequency returns. We study the finite sample properties of the estimation in a simulation study and apply it to...

We introduce a novel estimator of the quadratic variation that is based on the theory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in principle remove the effects of market...

This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a functional coefficient autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first order generalized...

The general theory of prediction-based estimating functions for stochastic process models is reviewed and extended. Particular attention is given to optimal estimation, asymptotic theory and Gaussian processes. Several examples of applications are presented. In particular partial observation of...

GARCH models have been successful in modeling financial returns. Still, much is to be gained by incorporating a realized measure of volatility in these models. In this paper we introduce a new framework for the joint modeling of returns and realized measures of volatility. The Realized GARCH...