On modelling the multivariate Realized Kernel financial time series

It is widely known that financial time series are characterized by very complex patterns and dynamics, that have to be accounting in estimation and forecasting analysis. Multivariate GARCH models have been and continue to be the most widely used time series models, both with parametric and non-parametric specifications: major examples are BEKK of Engle and Kroner (1995), the CCC of Bollerslev (1990) and the DCC of Engle (2002). Those models allow for volatility and correlations to change over time, and one of their main advantage is their easily implementation in many areas. More recently, the growing availability of high frequency data allows the development of different ex-post unbiased estimators of daily and intraday volatility, and this stimulated the development of specific models directly fitted on realized measures. Thus, although many multivariate variants of existing models could be applied on realized measures too, other specific models were adopted. Just to mention a few, the Realized GARCH of Hansen, Huang and Shek (2010), the Multiplicative Error Model of Engle (2002) and HEAVY models. Moreover, when multiple assets are involved, other issues arise (asynchronous trading and microstructure noise). Previous considerations underline the need for parametrizations and models able to guarantee the positiveness of variance covariance matrix at each point in time. As a natural consequence, the best choice is to adopt a Wishart distribution that automatically generates PSD matrices. Secondly, since the number of parameters to estimate clearly are proportionally to the number of assets included in the analysis, the estimation process could become infeasible. Thus, to overcome the curse-of- dimensionality problem that could arise, it is necessary to define several constraints in the models to estimate, however guaranteeing a high level of flexibility in the model parametrization. In view of this background, this thesis tries to contribute to the existing econometric literature, dealing with the estimation and the forecasts of variances, covariances and correlations on the basis of realized measures. After introducing some preliminary concepts about volatility and high frequency context, we introduced different model parametrizations that can be used in large dimensional systems. We relied some multiplicative models, based on the Wishart distribution, but with different structures, ranging from mean reverting models to others that are computationally intensive. Among others (vMEM, ReBEKK, Np-ReBEKK and HAR-DCC) we introduced a new parametrization that combine a multiplicative structure with dynamic correlations and variances, the DCC-CAW-MEM, directly fitted on the realized variance covariances matrices, computed through intra-daily data (5min RV), that has been tested both in the in-sample and out-of-sample scenarios.