A High-Order Hidden Markov Model and Its Applications for Dynamic Car Ownership Analysis

This paper extends the dynamically formulated hidden Markov models to a high-order hidden Markov model (HO-HMM) formulation. In the HO-HMM, the Markovian assumption that the future states (interpreted as the states of preferences or attitudes) depend only on the current state has been relaxed. Instead, the HO-HMM generalizes that the future states will depend on a number of states occurring beforehand. This paper develops the theoretical formulation of a HO-HMM framework. A recursive algorithm of likelihood computation is derived for model estimation. The algorithm significantly reduces the complexity of estimation and ensures the applicability of high-order hidden Markov modeling. The proposed methodology is further demonstrated on a vehicle ownership choice application using Puget Sound Transportation Panel data coupled with a few supplementary data sources. Long-term life-cycle stage changes in households are used as proxies for the high-order Markov transitions in car ownership hidden states. Results indicate that the HO-HMM has superior explanatory power in fitting longitudinal data.