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 e...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.展开更多
This study presents the uniform convergence rate for spot volatility estimators based on delta sequences.Kernel and Fourier-based estimators are examples of this type of estimator.We also present the uniform convergen...This study presents the uniform convergence rate for spot volatility estimators based on delta sequences.Kernel and Fourier-based estimators are examples of this type of estimator.We also present the uniform convergence rates for kernel and Fourier-based estimators of spot volatility as applications of the main result.展开更多
文摘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.
文摘This study presents the uniform convergence rate for spot volatility estimators based on delta sequences.Kernel and Fourier-based estimators are examples of this type of estimator.We also present the uniform convergence rates for kernel and Fourier-based estimators of spot volatility as applications of the main result.
