Asymptotic Normality of Convoluted Smoothed Kernel Estimation for Scalar Diffusion Model

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 Δ n → 0. The proce...

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Bibliographic Details
Published inMethodology and computing in applied probability Vol. 22; no. 1; pp. 191 - 221
Main Authors Song, Yuping, Hou, Weijie, Yang, Guang
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2020
Springer Nature B.V
Subjects
Asymptotic methods
Asymptotic properties
Business and Management
Computer simulation
Economic models
Economics
Electrical Engineering
Estimators
Life Sciences
Mathematics and Statistics
Monte Carlo simulation
Normality
Regression analysis
Statistics
Stock exchanges
Bias and variance reduction
62P20
Nonstationary high frequency financial data
Asymptotic normality
62M05
Diffusion models
Primary 62G20
Volatility function
Secondary 60J75
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Summary: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 Δ n → 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.
ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-019-09696-7