Multi-Horizon Mean-Covariance Estimation for Serial Correlated Returns

16 Pages Posted: 14 Oct 2019

See all articles by Zhuanxin Ding

Zhuanxin Ding

AlphaFocus Investment Research, LLC

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)

AlphaFocus Investment Research, LLC ( email )

P. O. Box 8306
Rancho Santa Fe, CA 92067
United States
1-858-461-1076 (Phone)

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