Central Limit Theorems of Local Polynomial Threshold Estimator for Diffusion Processes with Jumps. (19th February 2018)

• Record Type: Journal Article
• Authors: Song, Yuping; Wang, Hanchao
• Is Part Of: Scandinavian journal of statistics. Volume 45:Number 3(2018:Sep.)
• Page Start: 644
• Page End: 681
• Publication Date: 2018-02-19
• Subjects: central limit theorem -- diffusion processes with finite or infinite activity jumps -- Jacod's stable convergence theorem -- local polynomial threshold estimation; Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12318
• Languages: English
• ISSNs: 0303-6898

Abstract

Abstract: Central limit theorems play an important role in the study of statistical inference for stochastic processes. However, when the non‐parametric local polynomial threshold estimator, especially local linear case, is employed to estimate the diffusion coefficients of diffusion processes, the adaptive and predictable structure of the estimator conditionally on the σ ‐field generated by diffusion processes is destroyed, so the classical central limit theorem for martingale difference sequences cannot work. In high‐frequency data, we proved the central limit theorems of local polynomial threshold estimators for the volatility function in diffusion processes with jumps by Jacod's stable convergence theorem. We believe that our proof procedure for local polynomial threshold estimators provides a new method in this field, especially in the local linear case.