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Large Dynamic Covariance Matrix Estimation with an Application to Portfolio Allocation: A Semiparametric Reproducing Kernel Hilbert Space Approach

PENG Siyang1, GUO Shaojun2, LONG Yonghong1   

  1. 1. School of Mathematics, Renmin University of China, Beijing 100086, China;
    2. Institute of Statistics and Big Data, Renmin University of China, Beijing 100086, China
  • Received:2020-07-28 Revised:2021-05-06 Online:2022-08-25 Published:2022-08-02
  • Contact: GUO Shaojun,
  • Supported by:
    This paper was supported by National Natural Science Foundation of China under Grant No. 11771447.

PENG Siyang, GUO Shaojun, LONG Yonghong. Large Dynamic Covariance Matrix Estimation with an Application to Portfolio Allocation: A Semiparametric Reproducing Kernel Hilbert Space Approach[J]. Journal of Systems Science and Complexity, 2022, 35(4): 1429-1457.

The estimation of high dimensional covariance matrices is an interesting and important research topic for many empirical time series problems such as asset allocation. To solve this dimension dilemma, a factor structure has often been taken into account. This paper proposes a dynamic factor structure whose factor loadings are generated in reproducing kernel Hilbert space (RKHS), to capture the dynamic feature of the covariance matrix. A simulation study is carried out to demonstrate its performance. Four different conditional variance models are considered for checking the robustness of our method and solving the conditional heteroscedasticity in the empirical study. By exploring the performance among eight introduced model candidates and the market baseline, the empirical study from 2001 to 2017 shows that portfolio allocation based on this dynamic factor structure can significantly reduce the variance, i.e., the risk, of portfolio and thus outperform the market baseline and the ones based on the traditional factor model.
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