Realized Covariance Modeling with Adaptive Approach
Availability of high-frequency data made it possible to estimate covariance matrices of daily log returns. Among many existing methods, two scales realized volatility (TSRV) and two scales realized co-volatility (TSCV) have been used in this thesis. Chen, Härdle & Pigorsch (2009) proposed a localised procedure for modelling log-return variances. At each time point a past interval is determined which is used to approximate the variance by a simple dynamic model. The aim of this thesis is to extend this idea to the multivariate case. As in this case the number of parameters sharply increases with the number of analysed assets, a matrix factor model (MFM) is used to identify a lower dimensional factor process. In this thesis at each time point an MFM is estimated based on a suitable interval. We suggest methods to discover suitable estimation intervals. In the numerical analysis, the approximation quality of the adaptive MFM is analysed based on market data and simulation studies. The results are reasonable, even though the prediction results show that adaptive approaches can hardly improve the prediction quality compared to a simpler method.