Abstract
This paper presents the nonparametric estimation of first and second infinitesimal moments of the underlying jump-diffusion model with asymmetric kernel functions. In particular, we use asymmetric kernel estimators characterized by the gamma distribution. This approach allows to conciliate the idea of using the asymmetric kernel with jump-diffusion models. We show that the proposed estimators are consistent and asymptotically follow normal distribution under the conditions of recurrence and stationarity.
Highlights
Over the past few decades, nonparametric methods have become increasingly popular research fields e.g. statistics, economics, and probability communities, and such a trend undoubtedly will continue in future
The main advantage of the nonparametric methods is that they are helpful to estimate the coefficients of underlying model in a flexible way
We study the nonparametric estimation of infinitesimal moments of jump-diffusion models with asymmetric kernel functions
Summary
Over the past few decades, nonparametric methods have become increasingly popular research fields e.g. statistics, economics, and probability communities, and such a trend undoubtedly will continue in future. The main advantage of the nonparametric methods is that they are helpful to estimate the coefficients of underlying model in a flexible way. We study the nonparametric estimation of infinitesimal moments of jump-diffusion models with asymmetric kernel functions. Our approach allows us to conciliate the idea of using the asymmetric kernel functions and jump-diffusion models. We show that the proposed estimators are consistent and asymptotically follow normal distribution under the conditions of recurrence as well as for stationarity. The traditional kernel smoothing has been playing a wide role in estimating continuous-time diffusion processes since many years.
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