Discovering Hidden Structures Using Mixture Models: Application to Nonlinear Time Series Processes

This paper discuses the application of mixture models for analyzing data with hidden structure. More specifically, we are interested in situations where the structure is due to some unobserved factors. Detecting the latent structures in data is not trivial. On the other hand, since such structures could obscure the effect of the observed variables, ignoring them (e.g., using simple linear models) could result in wrong inference. To address this issue, we propose to use Dirichlet process mixtures. In this approach, the mixture identifier (i.e., the latent variable that assigns each component to a data point) acts as a surrogate for possible missing factors and provides insight into possible hidden structure in the data. An illustrative example is provided to show the usefulness of this approach. We also discuss the application of our method for analyzing time series processes that are subject to regime changes where there is no specific economic theory about the structure of the model.