Improving Econometric Forecasting: Functional Analytic Fixed Point Methods for Developing Hybridized Structural Models

Abstract

This paper is an exposition on the challenges of modern econometric modeling, and how econometric models either are too rigid or too unexplainable (Iskhakov, 2020; Kilic, 2025). We see this distinction much in the difference between traditional structural econometric models and machine learning models, where the traditional models often struggle for accuracy whereas the machine learning models struggle to output any real causal information (Iskhakov, 2020; Woloszyn & Bukowski, 2025). We develop a strong argument towards the use of hybrid models for econometric estimation rather than either option alone, models which address the weaknesses of both without developing any new major pitfalls (Buckmann et al., 2021; Lee, 2025). Within this paper, we also outline the necessary tools for the development of a type of model based on posing economic questions as inverse problems, which is well explored in Carrasco et al. (2007). This outline includes a summary of the inverse problems framework of Carrasco et al. (2007), an explanation of the Morozov Discrepancy Principle (Engl et al., 1996; Morozov, 1966, 1984) which is one of the key steps in the model, and finally an overview of our original model algorithm for recovering latent economic variables through estimation with Landweber regularization (Engl et al., 1996; Hanke et al., 1995; Landweber, 1951).