Factor State Space Modelling of the Ornstein-Uhlenbeck Process with Measurement Error and its Application

TL;DR

This paper introduces a factor-based multivariate Ornstein-Uhlenbeck state space model that effectively accounts for measurement error, addressing identifiability issues, and demonstrates its application to biological and environmental data.

Contribution

It extends the univariate OU state space model to a multivariate setting with a factor structure, resolving key estimation challenges and validating through real-world data analysis.

Findings

Successfully modeled gut microbiome dynamics with the new framework.

Analyzed North Atlantic SST data revealing latent temporal structures.

Validated the model's robustness through extensive simulations.

Abstract

Standard Ornstein-Uhlenbeck (OU) models often yield biased parameter estimates when measurement error is ignored. While the Ornstein-Uhlenbeck State Space Model (OUSSM) addresses this in univariate settings, multidimensional extensions remain limited. This paper introduces the factor OUSSM to model multi-dimensional, mean-reverting systems with observational noise. We resolve critical identifiability challenges in parameter estimation by establishing necessary constraints and validating the method through extensive simulations. We demonstrate the model's versatility by analyzing human gut microbiome dynamics and North Atlantic Sea Surface Temperature (SST) data. The results reveal distinct latent temporal structures in both biological and environmental systems, establishing the factor OUSSM as a robust framework for multivariate time series analysis.