Beyond Linearization: Automated Inference for Non-linear State Space Models – BLISS

The proposal addresses the need for advanced inference methods in economics and finance, focusing on dynamic non-linear models. Key application areas include forecasting inflation, estimating non-linear DSGE models, representing risk premia in macro-finance, and continuous-time modeling for derivative pricing. These models fall under the umbrella of non-linear state space models (SSMs) or hidden Markov models.

This project takes up the challenge of proposing a Bayesian estimation approach for such SSMs, particularly in scenarios with large time series, high-dimensional state spaces, complex nonlinearities, and highly informative observations, characteristic of the applications of interest. The proposed two-pronged approach involves methodological development and practical implementation. The goal is to create automated and efficient inference algorithms adaptable across diverse SSMs with minimal user intervention.
Current literature that relies on pseudo-marginalized methods, such as Sequential Monte Carlo, faces challenges in efficient likelihood estimates and inefficiencies in high-dimensional parameter spaces. The project builds on Controlled Sequential Monte Carlo routines but aims to enhance it by leveraging machine learning advances. Deep neural networks will be used to construct efficient SMC methods respecting the structure of SSMs. Neural networks will also be employed to provide efficient moves over the parameters.

The proposed methodology will be applied to the substantive applications in economics and finance, addressing the complexities of non-linear model solutions. The project aims to contribute to the widespread adoption of SSMs by automating and improving inference methods. The use of modern tools like automatic differentiation, stochastic gradient descent, and insights from reinforcement learning and variational inference literature is emphasized for a fully automated and efficient methodology.