Modeling of high-dimensional realized volatility matrices with financial applications

Abstract

With the availability of ultra-high-frequency data, it is possible to construct and model realized volatility and co-volatility nowadays and they have caught great attention. There are mainly three issues that should be considered when realized volatility/co-volatility is constructed, which is microstructure noise associated with high-frequency data, the asynchronicity of different assets and the high-dimensionality of the covariance matrix. In this thesis, the three issues are discussed and the high-dimensionality is mainly focused on. In Chapter 2, a brief literature review of the construction and modeling of realized volatility and co-volatility is provided. In Chapter 3, a spiked model for the high-dimensional realized covariance matrix is proposed which deals with the estimation of the spiked eigenvalues of the integrated covariance matrix when the dimension of the matrix is large. The proposed estimator is proved to be consistent and its nice empirical performance is presented. In addition, a factor Conditional Autoregressive Wishart model is proposed in Chapter 4 to model the high-dimensional realized covariance matrices. The proposed model reduces the number of parameters needed, ensures the positive-definiteness of the covariance matrix, and maintains a competitive forecasting ability compared to the existing model. Furthermore, the two higher order realized measures, namely realized skewness and kurtosis, are studied for their empirical properties in Chapter 5. It is found that the realized kurtosis has nice explanatory ability for the future volatility, confirmed by extensive data analysis.