大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Nadaraya-Watson estimator for stochastic processes driven by stable Levy motions

Hongwei Long (Florida Atlantic University)

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4. Nadaraya-Watson estimator for stochastic processes driven by stable Levy motions

大阪大学 金融・保険セミナーシリーズ 第41回(CSFI-CRESTジョイントセミナー)

Nadaraya-Watson estimator for stochastic processes driven by stable Levy motions

Hongwei Long (Florida Atlantic University)

We discuss the nonparametric Nadaraya-Watson (N-W) estimator of the drift function for ergodic stochastic processes driven by stable noises and observed at discrete instants. Under geometrical mixing condition, we derive consistency and rate of convergence of the N-W estimator of the drift function. Furthermore, we obtain a central limit theorem for stable stochastic integrals. The central limit theorem has its own interest and is a crucial tool for the proofs. A simulation study illustrates the finite sample properties of the N-W estimator.