关键词: 高维时变投资组合, DCC-MIDAS-NL模型, QuEST函数, 非线性收缩法

Abstract: In the era of big data, with the improvement of data availability, the dimension of financial data has exploded. Due to the increasing number of assets possessed by financial institutions or individuals, it is very common for many individuals and financial institutions to construct high-dimensional financial portfolios. Therefore, one major hot-spot and difficult issue in the field of statistics and finance is how to estimate and predict the risk of large portfolios. At present, the research on the risk of such portfolios primarily focuses on two issues: first, how to effectively estimate and predict the covariance matrix between high-dimensional assets that play a pivotal role in the portfolio; second, how to introduce the penalty function to construct a portfolio model with constraint conditions. Based on the previous research, this paper puts forward a new model to estimate and predict the covariance matrix between high-dimensional assets, so as to improve the efficiency of estimating and predicting the covariance matrix, and further explore the influence of the introduction of the penalty function on portfolio efficiency. Thus, we can more accurately analyze and describe the risk of high-dimensional portfolios. In conclusion, the research in this paper possesses significant intellectual merit.
The DCC-MIDAS model is an upgrade of the DCC model. Although it can improve the estimation efficiency to some extent, like the DCC model, it is also influenced by the curse of dimensionality, leading to a less effective estimation and prediction of the high-dimensional covariance matrix. Therefore, in this paper, we apply the QuEST function and the nonlinear shrinkage method to the estimation of the DCC-MIDAS model to advance it, thus proposing the DCC-MIDAS-NL model to overcome the deficiency of the DCC-MIDAS model. It mainly has two advantages: Firstly, the DCC-MIDAS-NL model can effectively solve the curse of dimensionality and overcome the deficiency of the DCC-MIDAS model, enabling easier access to the estimation and prediction of high-dimensional time-varying portfolios. Secondly, in the DCC-MIDAS-NL model, we don’t need to assume that the data follow the normal distribution, which is exactly consistent with reality, for the reason that the yield data of financial assets often have the characteristics of higher peak and fat tail. Therefore, the DCC-MIDAS-NL model theoretically gets the upper hand. In addition, this paper would introduce a variety of penalty functions into the minimum variance portfolio model to discuss the application effect of the DCC-MIDAS-NL model in the portfolio and the influence of the penalty functions on portfolio efficiency.
The following conclusions can be drawn from the research in this paper: (1)When the dimensionality of assets is high, the covariance matrix between financial assets estimated and predicted by the DCC-MIDAS-NL will have a better application effect in the portfolio than that in the portfolio estimated and predicted by the DCC-MIDAS and the commonly used NLS model. Regardless of the type of portfolio, the DCC-MIDAS-NL model corresponds to higher returns, lower risk, and higher utility function values. The reason is that it can better estimate the covariance matrix between financial assets with the characteristics of higher peak and fat tail, so as to effectively improve the efficiency of the portfolio, and meanwhile, effectively solve the dimensionality curse problem without the assumption of normal distribution. (2)Compared to the original minimum variance portfolio MVP, the MVP-C, MVP-LASSO, and MVP-W portfolios that introduce the penalty function have good performance. This shows that when the dimensionality of assets is rather high, introducing the penalty function can effectively solve the dimensionality curse problem and improve portfolio efficiency. (3)For low-dimensional assets, the estimation effect of the DCC-MIDAS model is better than that of the DCC-MIDAS-NL model. This demonstrates that the DCC-MIDAS-NL model put forward in this paper is more applied to high-dimensional assets, and the higher the dimensionality of the assets the better the estimation effect of the DCC-MIDAS-NL model.

Key words: high dimensional time-varying portfolio, DCC-MIDAS-NL model, QuEST function, nonlinear shrinkage method