Nonparametric Estimation for Recurrent Jump-Diffusion Models

论文摘要

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）.

论文目录

• ACKNOWLEDGEMENTS
• Preface
• Abstract
• Content
• Chapter 1 Introduction and preliminaries
• 1.1 Introduction
• 1.1.1 Background of the thesis
• 1.1.2 General notations
• 1.2 Preliminaries
• 1.2.1 Diffusion models with jumps
• 1.2.2 Recurrence
• 1.2.3 Local time
• 1.3 Nonparametric methods
• 1.3.1 Review of the statistical inference
• 1.3.2 Nadaraya-Watson estimator
• 1.3.3 Local linear estimator
• 1.3.4 Reweighted Nadaraya-Watson estimator
• 1.3.5 Empirical likelihood method
• 1.3.6 Local time estimator
• Chapter 2 Local linear estimation of recurrent jump-diffusion models
• 2.1 Introduction
• 2.2 Jump-diffusion model and local linear estimator
• 2.3 Assumptions and main Results
• 2.4 Proofs
• Chapter 3 Reweighted Nadaraya-Watson estimation of jump-diffusion models
• 3.1 Introduction
• 3.2 Jump-diffusion model and reweighted Nadaraya-Watson estimator
• 3.3 Some assumptions and useful preliminaries
• 3.4 Proof
• 第四章 Further work
• 4.1 Nonparametric inference of jump-diffusion models by using asym-metric kernels
• 4.2 Local linear estimation of scalar diffusion models by using asym-metric kernels
• 4.3 Reweighted Nadaraya-Watson estimation of scalar diffusion mod-els by using asymmetric kernels
• 第五章 Future work
• 参考文献
• Completed Papers