Towards Prediction of Nonlinear and Nonstationary Evolution of Customer Preferences Using Local Markov Models
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A dynamic vehicle design process hinges on one's ability to forecast how the customer preferences and the exogenous variables evolve over time. Prior research mentions and it is understood in practice that the dynamics of evolution of these variables is highly nonstationary, and can be nonlinear. This paper aims to provide a mathematical model based on Markov models for predicting future states of such nonlinear nonstationary dynamic processes. The state space of a dynamic system is reconstructed from the historic data using delay embedding principles, and a Markov model is derived therefrom. The reconstructed state space is clustered into different neighborhoods to form nodes of a graph by using a set covering formulation. The probabilities of transition between every node-pair were obtained for this graph. Next, the system trajectory is segmented into multiple near-stationary time intervals based on pattern analysis of the transition matrix. Assuming stationary behavior of the system within each segment, the corresponding Markov transition matrix can be used for prediction inside that segment. Due to the proprietary nature of actual customer preference data, the present model was validated using swapped Rossler attractor data as well as a time-series data that mimics, in the sense of nonlinear and nonstationary patterns, the trends of willingness to pay (WTP) data acquired for a customer group for particular sets of vehicles in a portfolio. One and five step ahead prediction results indicates that the proposed model is 5-25% more accurate (in terms of R2 statistic) than the models commonly used in practice. © Springer Science+Business Media B.V. 2009.
author list (cited authors)
Bukkapatnam, S., Yang, H., & Madhavi, F.