Abstract
We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations. The estimates, based on either the continuously observed process or the discretely observed process, are considered. Under certain conditions, we prove the strong consistency and the asymptotic normality of the two estimators. Our method is also suitable for one-sided reflected stochastic differential equations. Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis et al. (Stat Sin, 2021, 31: 29–51). Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.
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This work was partially supported by the National Natural Science Foundation of China (11871244), and the Fundamental Research Funds for the Central Universities, JLU.
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Han, Y., Zhang, D. Nadaraya-Watson estimators for reflected stochastic processes. Acta Math Sci 44, 143–160 (2024). https://doi.org/10.1007/s10473-024-0107-1
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DOI: https://doi.org/10.1007/s10473-024-0107-1
Key words
- reflected stochastic differential equation
- discretely observed process
- continuously observed process
- Nadaraya-Watson estimator
- asymptotic behavior