This paper considers linear rational expectations models in the frequency domain under general conditions. The paper develops necessary and sufficient conditions for existence and uniqueness of particular and generic systems and characterizes the space of all solutions as an affine space in the frequency domain. It is demonstrated that solutions are not generally continuous with respect to the parameters of the models, invalidating mainstream frequentist and Bayesian methods. The ill-posedness of the problem motivates regularized solutions with theoretically guaranteed uniqueness, continuity, and even differentiability properties. Regularization is illustrated in an analysis of the limiting Gaussian likelihood functions of two analytically tractable models.

翻译：本文在一般条件下从频域角度研究线性理性预期模型。本文推导出特定系统与通用系统解存在且唯一的充要条件，并将所有解的空间刻画为频域中的一个仿射空间。研究表明，解通常不随模型参数连续变化，这使得主流频率学派与贝叶斯方法失效。问题的病态性催生了正则化解法，这类解法在理论上具有唯一性、连续性乃至可微性保证。通过对两个解析可处理模型的极限高斯似然函数进行分析，本文阐释了正则化的应用。