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 DSGE models, affine term structure models, and trend-cycle decomposition illustrate the methodology and the results.

翻译：本文考虑潜在动态误设定的状态空间模型中的滤波、参数估计与检验问题。当动态过程被误设定时，状态变量的滤波值通常不满足模型约束，导致其难以解释，且参数估计可能无法刻画滤波变量的动态特征。为解决这一问题，采用序列最优传输方法，通过将观测值从灵活简化形式迭代映射到结构条件分布，生成模型一致的样本。由生成样本得到的滤波序列满足模型一致性。针对线性过程，推导出闭式最优传输滤波算法。通过最小化生成观测值与实际观测值之间的差异，定义了最优传输估计量，并推导了其大样本性质。一项设定检验用于判断模型能否复现样本路径，或差异是否具有统计显著性。通过对DSGE模型、仿射期限结构模型及趋势-周期分解的经验应用，展示了该方法及相应结果。