Vine copula base modelling and forecasting of multivariate realized volatility time-series

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Reliable forecasts of stock market volatility are necessary in portfolio management and the evaluation of risks. Due to the increasing availability of high-frequency data, the use of squared returns to estimate the ex-post realized volatility (RV) has become one of the standard methods in empirical finance.Within the project we will tackle both the modeling approaches for univariate times series of realized variances and for matrix variate time series of realized covariance matrices. The currently most popular univariate model for realized volatility modeling is the HAR regression. The performance of the model is convincing, but the choice of the explanatory factors (measured at daily frequency) in the model is merely heuristic. Within the first part of the project we addressed the nonlinear modeling of temporal dependence of the factors. In the second phase of the project we will concentrate on statistical approaches such as principle component analysis, factor analysis and neural networks, which will help us to determine the optimal aggregation of historical data for factor building. Similar problem remains if we consider the initial intraday information. The realized volatilities are estimated in the simplest case using the sum of squared intra-day returns. It is of key interest to address the proper aggregation and transformation of intra-day returns too.The method we advocated for the realized covariance matrices in the first phase of the project was based on partial correlations. It shows good performance, but we would like to improve further its performance and ensure more robust forecasts. For this we want to investigate a new selection method which chooses the subset of standard and partial correlations, which form the partial correlation vine, based on the forecasting performance of the marginal models associated to the univariate partial correlation time-series. We expect that this way of proceeding will lead to an improved forecasting performance. So far we have not considered model sparsity of the partial correlation vines. In general, model sparsity in a vine copula model can be achieved by setting certain pair-copulas to the independence copula. This corresponds to a partial correlation value of zero in a partial correlation vine. So-called truncated vines set all pair-copulas of trees above a certain level to the independence copula. We will study several choices of setting this truncation level.