We derive the asymptotic distribution for the LU decomposition, that is, the Cholesky decomposition, of realized covariance matrix. Distributional properties are combined with an existing generalized heterogeneous autoregressive (GHAR) method for forecasting realized covariance matrix, which will be referred to as a generalized HARQ (GHARQ) method. An out-of-sample forecast comparison of a real data set shows that the proposed GHARQ method outperforms other existing methods in terms of optimizing the variances of portfolios.
Bibliographical noteFunding Information:
The authors are very thankful for the valuable comments of a referee which improve the article considerably. This research is supported by a grant from the National Research Foundation of Korea (2016R1A2B4008780)
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- Cholesky decomposition
- LU decomposition
- minimum variance portfolio
- portfolio optimization
- realized covariance