Asymptotic Normality of Convoluted Smoothed Kernel Estimation for Scalar Diffusion Model

Yuping Song (), Weijie Hou and Guang Yang
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Yuping Song: Shanghai Normal University
Weijie Hou: Shanghai Normal University
Guang Yang: Shanghai Normal University

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 1, 191-221

Abstract: Abstract In this paper, we consider a convoluted smoothed nonparametric approach for the unknown coefficients of diffusion model based on high frequency data. Under regular conditions, we obtain the asymptotic normality for the proposed estimators as the time span T →∞ and sample interval Δn → 0. The procedure and asymptotic behavior can be applied for both Harris recurrent and positive Harris recurrent processes. The finite-sample benefits of the underlying estimators are verified through Monte Carlo simulation and 15-min high-frequency stock index in Shanghai Stock Exchange for an empirical application.

Keywords: Diffusion models; Volatility function; Asymptotic normality; Bias and variance reduction; Nonstationary high frequency financial data; Primary 62G20; 62M05; Secondary 60J75; 62P20 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11009-019-09696-7

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