A Functional Data Approach for Continuous-Time Analysis Subject to Modeling Discrepancy under Infill Asymptotics

Tao Chen (), Yixuan Li and Renfang Tian
Additional contact information
Tao Chen: Department of Economics, Cross Appointed to Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Yixuan Li: Big Data Research Lab, University of Waterloo, Waterloo, ON N2L 3G1, Canada
Renfang Tian: Big Data Research Lab, University of Waterloo, Waterloo, ON N2L 3G1, Canada

Mathematics, 2023, vol. 11, issue 20, 1-27

Abstract: 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.

Keywords: continuous-time analysis; frequency-dependent parameter; functional data analysis; infill asymptotics; modeling discrepancy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/20/4386/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/20/4386/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:20:p:4386-:d:1264898

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().