TITLE:
The Estimation of the Spot Volatility for Diffusion Process
AUTHORS:
Weiwei Xu, Xin Yang, Shanchao Yang
KEYWORDS:
Diffusion Process, Spot Volatility, GM Type Estimation, Asymptotic Property
JOURNAL NAME:
Open Journal of Statistics,
Vol.11 No.2,
April
21,
2021
ABSTRACT: In this
paper, we propose a Gasser-Müller type spot volatility estimator (abbreviated
as GM type estimator) for diffusion process, which is weighted by integrals, it
is different from the kernel spot volatility estimator discussed by Kristensen
(2010). Under more general conditions, the asymptotic unbiasedness and the
asymptotic normality of the GM type estimator are derived. The simulation
results show that the GM type spot volatility estimator has good estimation
effect, and its mean square error tends to be less than that of the kernel spot
volatility estimator discussed by Kristensen (2010), so it provides a selection
method for estimating the spot volatility in high frequency data environment.