Google Summer of Code 2025

Abstract

State-space models (SSMs) provide a flexible framework for modeling dynamic systems where latent states evolve over time. In econometrics, Dynamic Factor Models (DFMs) are widely used to capture the co-movement of multiple time series by assuming that a small number of latent factors drive the observed variables. The PyMC library already includes implementations of SARIMAX, VARMAX, and structural state-space models, along with example notebooks for their usage. This project aims to extend the existing PyMC state-space module by implementing Dynamic Factor Models, aligning with the functionality available in Statsmodels.

In Statsmodels, our reference for the development of the project, two DFM implementations exist: DynamicFactor, which represents the model in state-space form and estimates parameters via Kalman filtering, and DynamicFactorMQ, based on the Expectation-Maximization (EM) algorithm. Our implementation will follow a Bayesian approach by leveraging PyMC’s probabilistic programming framework and PyTensor for computation. Additionally, an accompanying example notebook will demonstrate estimation, forecasting, and causal analysis with the new model, ensuring accessibility for users with varying levels of experience in Bayesian modeling.