Multi-Horizon Mean-Covariance Estimation for Serial Correlated Returns

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.