Open Access
August 2019 Asymptotically efficient estimators for self-similar stationary Gaussian noises under high frequency observations
Masaaki Fukasawa, Tetsuya Takabatake
Bernoulli 25(3): 1870-1900 (August 2019). DOI: 10.3150/18-BEJ1039


This paper proposes feasible asymptotically efficient estimators for a certain class of Gaussian noises with self-similarity and stationarity properties, which includes the fractional Gaussian noises, under high frequency observations. In this setting, the optimal rate of estimation depends on whether either the Hurst or diffusion parameters is known or not. This is due to the singularity of the asymptotic Fisher information matrix for simultaneous estimation of the above two parameters. One of our key ideas is to extend the Whittle estimation method to the situation of high frequency observations. We show that our estimators are asymptotically efficient in Fisher’s sense. Further by Monte-Carlo experiments, we examine finite sample performances of our estimators. Finite sample modifications of the asymptotic variances of the estimators are also given, which exhibit almost perfect fits to the numerical results.


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Masaaki Fukasawa. Tetsuya Takabatake. "Asymptotically efficient estimators for self-similar stationary Gaussian noises under high frequency observations." Bernoulli 25 (3) 1870 - 1900, August 2019.


Received: 1 August 2017; Revised: 1 March 2018; Published: August 2019
First available in Project Euclid: 12 June 2019

zbMATH: 07066243
MathSciNet: MR3961234
Digital Object Identifier: 10.3150/18-BEJ1039

Keywords: Asymptotic efficiency , fractional Gaussian noises , high frequency observations , local asymptotic normality , Whittle estimation

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

Vol.25 • No. 3 • August 2019
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