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

Dong Mei Zhu, Jiejun Lu*, Wai Ki Ching, Tak Kuen Siu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)223-232
Number of pages10
JournalEconomic Modelling
Publication statusPublished - 1 Nov 2017


  • Expectation-Maximization (EM) Algorithm
  • Higher-Order Autoregressive Hidden Markov Model (HO-HMMAR)
  • Optimal asset allocation
  • Utility maximization
  • Model (HO-HMMAR)


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