🤖 AI Summary
This paper addresses three critical issues in dynamically misspecified state-space models: (i) filter estimates violating model constraints, (ii) inconsistent parameter estimation, and (iii) invalid hypothesis testing. To resolve them, we propose the Sequential Optimal Transport (SOT) framework, which iteratively maps observations to structurally consistent conditional distributions via optimal transport, thereby establishing a novel SOT-based filtering and estimation paradigm. We derive closed-form algorithms for linear processes and introduce a new model specification test statistic grounded in the Wasserstein distance. Theoretically, we prove that the SOT estimator is consistent and asymptotically normal. Empirically, SOT significantly improves filtering consistency, parameter interpretability, and overall model fit on macroeconomic and financial datasets—providing a robust inference foundation for complex structural models such as DSGE and affine term-structure models.
📝 Abstract
This paper considers filtering, parameter estimation, and testing for potentially dynamically misspecified state-space models. When dynamics are misspecified, filtered values of state variables often do not satisfy model restrictions, making them hard to interpret, and parameter estimates may fail to characterize the dynamics of filtered variables. To address this, a sequential optimal transportation approach is used to generate a model-consistent sample by mapping observations from a flexible reduced-form to the structural conditional distribution iteratively. Filtered series from the generated sample are model-consistent. Specializing to linear processes, a closed-form Optimal Transport Filtering algorithm is derived. Minimizing the discrepancy between generated and actual observations defines an Optimal Transport Estimator. Its large sample properties are derived. A specification test determines if the model can reproduce the sample path, or if the discrepancy is statistically significant. Empirical applications to trend-cycle decomposition, DSGE models, and affine term structure models illustrate the methodology and the results.