Multi-Horizon Mean-Covariance Estimation for Serial Correlated Returns

16 Pages Posted: 14 Oct 2019

Date Written: October 1, 2019


Assume asset returns follow a VARMA_MARCH structure, this paper derives the proper multi-horizon mean and covariance matrix estimations that can be used as inputs to mean-variance optimization problem for investors with different horizons. The result is further extended to vector error-correction model with GARCH errors. A simple example is given to show the significant impact of serial correlation to multi-horizon volatility and correlation estimation in asset allocation study. The result can also be applied to calculate multi-horizon volatility estimation for option trading purposes when the underlying model is built upon high frequency data.

Keywords: multi-horizon mean and covariance matrix, serial correlation, time aggregation, asset allocation

JEL Classification: G, C1, C2, C6

Suggested Citation

Ding, Zhuanxin, Multi-Horizon Mean-Covariance Estimation for Serial Correlated Returns (October 1, 2019). Available at SSRN: or

Zhuanxin Ding (Contact Author)

Bloomberg LP ( email )

731 Lexington Avenue
New York, NY 10022
United States
1-415-281-6340 (Phone)

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