NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES*

doi:10.1007/s10473-024-0107-1

Abstract

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.

Key words: reflected stochastic differential equation, discretely observed process, continuously observed process, Nadaraya-Watson estimator, asymptotic behavior

CLC Number:

60F15

Yuecai Han, Dingwen Zhang. NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES^*[J].Acta mathematica scientia,Series B, 2024, 44(1): 143-160.

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NADARAYA-WATSON ESTIMATORS FOR REFLECTED STOCHASTIC PROCESSES^*

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