Measuring dependence in a multivariate time series is tantamount to modelling its dynamic structure in space and time. In the context of a multivariate normally distributed time series, the evolution of the covariance (or correlation) matrix over time describes this dynamic. A wide variety of...

For a Lévy process X having finite variation on compact sets and finite first moments, µ( dx) = xv( dx) is a finite signed measure which completely describes the jump dynamics. We construct kernel estimators for linear functionals of µ and provide rates of convergence under regularity...

An efficient estimator is constructed for the quadratic covariation or integrated covolatility matrix of a multivariate continuous martingale based on noisy and non-synchronous observations under high-frequency asymptotics. Our approach relies on an asymptotically equivalent continuous-time...

We consider noisy non-synchronous discrete observations of a continuous semimartingale. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: onedimensional for the spectral estimator of integrated volatility, from two-dimensional asynchronous...

There is increasing demand for models of time-varying and non-Gaussian dependencies for mul- tivariate time-series. Available models suffer from the curse of dimensionality or restrictive assumptions on the parameters and the distribution. A promising class of models are the hierarchical...

We consider the problem of estimating the conditional quantile of a time series fYtg at time t given covariates Xt, where Xt can ei- ther exogenous variables or lagged variables of Yt . The conditional quantile is estimated by inverting a kernel estimate of the conditional distribution function,...

Financial risk control has always been challenging and becomes now an even harder problem as joint extreme events occur more frequently. For decision makers and government regulators, it is therefore important to obtain accurate information on the interdependency of risk factors. Given a...

This study proposes a novel framework for the joint modelling of commodity forward curves. Its key contribution is twofold. First, dynamic correlation models are applied in this context as part of the modelling scheme. Second, we introduce a family of dynamic conditional correlation models based...

Portfolio selection and risk management are very actively studied topics in quantitative finance and applied statistics. They are closely related to the dependency structure of portfolio assets or risk factors. The correlation structure across assets and opposite tail movements are essential to...

The Value-at-Risk calculation reduces the dimensionality of the risk factor space. The main reasons for such simplifications are, e.g., technical efficiency, the logic and statistical appropriateness of the model. In Chapter 2 we present three simple mappings: the mapping on the market index,...