Abstract
Estimation of a conditional covariance matrix is an interesting and important research topic in statistics and econometrics. However, modelling ultra-high dimensional dynamic (conditional) covariance structures is known to suffer from the curse of dimensionality or the problem of singularity. To partially solve this problem, this paper establishes a model by combining the ideas of a factor model and a symmetric GARCH model to describe the dynamics of a high-dimensional conditional covariance matrix. Quasi maximum likelihood estimation (QMLE) and least square estimation (LSE) methods are used to estimate the parameters in the model, and the plug-in method is introduced to obtain the estimation of conditional covariance matrix. Asymptotic properties are established for the proposed method, and simulation studies are given to demonstrate its performance. A financial application is presented to support the methodology.
Highlights
Estimation of a conditional covariance matrix is an important and popular topic in statistics and econometrics with wide applications in many disciplines, such as engineering, environmentology, psychology, economics and finance
These GARCH models can be called symmetric GARCH models, which assume that the response of conditional covariance to a shock is a function of the shock strength only without any correlation with the sign of the shock
To capture the leverage effects, some multivariate GARCH models take into account negative shocks with a larger impact on their conditional covariance compared with positive shocks of the same absolute value
Summary
Estimation of a conditional covariance matrix is an important and popular topic in statistics and econometrics with wide applications in many disciplines, such as engineering, environmentology, psychology, economics and finance. Common multivariate GARCH models cannot be directly applied to ultrahigh dimensional data, which is often the case when constructing a portfolio allocation in finance This is because there are too many parameters to be estimated when the dimension is large, see, e.g., [9]. O-GARCH model as a special case of [21] is a successful multivariate GARCH model with a parsimonious form This captures the dynamics of conditional covariance but can reduce the dimensions effectively if the model is identified fairly. [23] proposed a dynamic structure and developed an estimation procedure for high-dimensional conditional covariance matrices. Motivated by the above literature, we propose an alternative model for estimating high-dimension conditional covariance matrix.
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