A functional data approach for continuous-time analysis subject to modeling discrepancy under infill asymptotics
Author
Faculty Advisor
Date
2023
Keywords
continuous-time analysis, frequency-dependent parameter, functional data analysis, infill asymptotics, modeling discrepancy
Abstract (summary)
Parametric continuous-time analysis often entails derivations of continuous-time models from predefined discrete formulations. However, undetermined convergence rates of frequency-dependent parameters can result in ill-defined continuous-time limits, leading to modeling discrepancy, which impairs the reliability of fitting and forecasting. To circumvent this issue, we propose a simple solution based on functional data analysis (FDA) and truncated Taylor series expansions. It is demonstrated through a simulation study that our proposed method is superior—compared with misspecified parametric methods—in fitting and forecasting continuous-time stochastic processes, while the parametric method slightly dominates under correct specification, with comparable forecast errors to the FDA-based method. Due to its generally consistent and more robust performance against possible misspecification, the proposed FDA-based method is recommended in the presence of modeling discrepancy. Further, we apply the proposed method to predict the future return of the S&P 500, utilizing observations extracted from a latent continuous-time process, and show the practical efficacy of our approach in accurately discerning the underlying dynamics.
Publication Information
Chen, T., Li, Y., & Tian, R. (2023). A functional data approach for continuous-time analysis subject to modeling discrepancy under infill asymptotics. Mathematics, 11(20), 4386. https://doi.org/10.3390/math11204386
Notes
Item Type
Article
Language
Rights
Attribution (CC BY)
