Nonparametric Estimation for Recurretn Jump-Diffusion Models

摘要

This work describes the nonparametric estimation of infinitesimal momentsof jump-diffusion models. The local linear and reweighted Nadaraya-Watson estimators were used to study the recurrent jump-diffusion models. During thestudies, it was noted that under mild conditions the nonparametric estimationsof infinitesimal moments based on the local linear estimator and reweightedNadaraya-Watson are consistent and asymptotically follow the normal distributions. The special attention was paid to the infinite jump activity case. Theasymptotic normality results in our case are found more complex than the usualones. Usually, researchers have been using nonrandom factor as a normalizedfactor. However, we used a random variable as a normalized factor since our processes are non stationary. Our results are more complex and can be implied to theusual case. We conclude that, using the local linear estimator and the reweightedNadaraya-Watson estimator of infinitesimal moments for jump-diffusion model,our results improve the results of Bandi and Nguyen (2003) and Xu (2003).