Discrete-time optimal asset allocation under Higher-Order Hidden Markov Model

This paper studies an optimal portfolio selection problem under a discrete-time Higher-Order Hidden Markov-Modulated Autoregressive (HO-HMMAR) model for price dynamics. By interpreting the hidden states of the modulating higher-order Markov chain as different states of an economic condition, the model discussed here may incorporate the long-term memory of economic states in modeling price dynamics and optimal asset allocation. The estimation of an estimation method based on Expectation-Maximization (EM) algorithm is used to estimate the model parameters with a view to reducing numerical redundancy. The asset allocation problem is then discussed in a market with complete information using the standard Bellman's principle and recursive formulas are derived. Numerical results reveal that the HO-HMMAR model may have a slightly better out-of-sample forecasting accuracy than the HMMAR model over a short horizon. The optimal portfolio strategies from the HO-HMMAR model outperform those from the HMMAR model without long-term memory in both real data and simulated data experiments.