A Matrix‐Based Hidden Markov Model for Consumer Credit Analysis

This paper introduces a novel hidden Markov variant, the matrix‐based hidden Markov model (MHMM), which characterizes mixture of Markov chains whose transition matrices are governed stochastically by unobservable states. By offering a multi‐scale, hierarchical framework for stochastic dynamics, the model enables improved inference of structured hidden states (i.e., the hidden transition matrices) and their underlying generative mechanism from non‐homogeneous time series data. The paper presents efficient algorithms for parameter estimation and hidden path inference. Besides, we introduce the absorbing matrix‐based hidden Markov model (AMHMM), incorporating absorbing states into the framework. Through Markov absorption theory, we analyze the model's pre‐absorption behavior. A numerical example, based on simulated consumer repayment data, illustrates the value of the AMHMM: It provides estimates of default timing, reveals propensity for overdue installments and behavioral patterns, and helps assess the overall trend in the credit environment.