Nonparametric Estimation For Recurrent Jump-diffusion Models

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