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

We discuss the nonparametric Nadaraya-Watson (N-W) estimator of the drift function for ergodic stochastic processes driven by α-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 the crucial tool for the proofs. A simulation study illustrates the finite sample properties of the N-W estimator. AMS 2000 subject classification. 60G52, 62G20, 62M05, 65C30

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