A study on modeling of the realized covariance matrices

Abstract

This thesis studies the modeling of realized covariance (RCOV) matrices. A new type of parametric model is introduced, which might illuminate new approaches to inferences on multivariate volatility models in time series analysis. The traditional multivariate volatility models have been extensively discussed, including multivariate ARCH and GARCH models. However, most of these models are studying the hidden covariance structure based on the vector of low frequency returns. With the availability of high frequency data, this thesis utilizes RCOV matrices which can be explicitly estimated from data and have been acknowledged as a promising estimator of the covariance structure of lower frequency returns. While there are pioneer researchers working on modeling of RCOV matrices, existing methods depend largely on the normality assumptions and Wishart matrix processes. This thesis adopts an alternative distribution, the matrix-F distribution, to accommodate heavy tailed data. Apart from the classical MLE, variance targeting is proposed to deal with estimation difficulties and over-parametrizations. Stationarity conditions and asymptotic properties are also constructed for the models. In addition, this thesis also proposes two diagnostic tests for the proposed models, where the estimation effects are included. When faced with high dimensional RCOV matrices, this thesis also suggests using of a matrix factor model for dimension reduction. Asymptotic properties of the proposed method has been established in this work. Monte-carlo simulations are conducted to evaluate finite sample performance of the constructed methods. Real applications have been conducted on stock price data from DJIA indexes and S&P500 indexes. (245 words)