Parametric Estimation of Diffusion Processes: A Review and Comparative Study

Alejandra López-Pérez, Manuel Febrero-Bande and Wencesalo González-Manteiga
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Alejandra López-Pérez: Department of Statistics, Mathematical Analysis and Optimization, University of Santiago de Compostela, Rúa de Lope Gómez de Marzoa s/n, 15705 Santiago de Compostela, Spain
Manuel Febrero-Bande: Department of Statistics, Mathematical Analysis and Optimization, University of Santiago de Compostela, Rúa de Lope Gómez de Marzoa s/n, 15705 Santiago de Compostela, Spain
Wencesalo González-Manteiga: Department of Statistics, Mathematical Analysis and Optimization, University of Santiago de Compostela, Rúa de Lope Gómez de Marzoa s/n, 15705 Santiago de Compostela, Spain

Mathematics, 2021, vol. 9, issue 8, 1-27

Abstract: This paper provides an in-depth review about parametric estimation methods for stationary stochastic differential equations (SDEs) driven by Wiener noise with discrete time observations. The short-term interest rate dynamics are commonly described by continuous-time diffusion processes, whose parameters are subject to estimation bias, as data are highly persistent, and discretization bias, as data are discretely sampled despite the continuous-time nature of the model. To assess the role of persistence and the impact of sampling frequency on the estimation, we conducted a simulation study under different settings to compare the performance of the procedures and illustrate the finite sample behavior. To complete the survey, an application of the procedures to real data is provided.

Keywords: diffusion processes; continuous-time models; parametric estimation; stochastic differential equations; SDE (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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