Local linear estimator for stochastic differential equations driven by α-stable Lévy motions

2012/04/06 by Song Yu-Ping, Yu-Ping, Song, Zhengyan Lin +2
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Stability and Controllability of Differential Equations #Statistics Theory (math.ST) #Stochastic processes and financial applications #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1204.1454

15 pages

arxiv created 2012/04/06 · openalex publication_date 2012/04/06 · arxiv updated 2012/04/09 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

We study the local linear estimator for the drift coefficient of stochastic differential equations driven by α-stable Lévy motions observed at discrete instants letting T → ∞. Under regular conditions, we derive the weak consistency and central limit theorem of the estimator. Compare with Nadaraya-Watson estimator, the local linear estimator has a bias reduction whether kernel function is symmetric or not under different schemes.

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