Since the introduction of ARCH models close to 40 years ago, a wide range of models for volatility estimation and prediction have been developed and integrated into asset allocation, financial derivative pricing, and financial risk management. Research has also been very active in extending volatility modeling to dependence modeling and in developing our understanding of risk and uncertainty in financial systems. This paper presents a review on the statistical modeling on volatility and dynamic dependence of financial returns. In addition, we present a real data example using a time-varying copula model to estimate the dynamic dependence of stock returns. Research on volatility and dynamic dependence modeling will continue to encounter statistical and computational challenges; it is necessary to persist in dealing with the 3H (high dimension, high frequency, high complexity) paradigm in modeling. This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods

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In this article, we extend the skew-t data perturbation (STDP) to develop a new statistical disclosure control (SDC) method for data with continuous variables. In this new SDC method, we construct an extended skew-t (EST) copula to release confidential data for third-party usage. Using the EST copula for producing perturbed data, we can incorporate rich statistical information in the perturbed data while preserving the marginal distributions of the data. An advancement of this EST-SDC method is to use a copula distribution, which allows generation of perturbed data from bivariate conditional EST copulas sequentially. We discuss the methodology of EST-SDC and outline some statistical properties derived from copula theories. Simulations and a real data study are included to demonstrate how the EST-SDC method can be applied and to compare with the STDP method.