Minimum contrast estimator for fractional Ornstein-Uhlenbeck processes

2012 ◽  
Vol 55 (7) ◽  
pp. 1497-1511 ◽  
Author(s):  
WeiLin Xiao ◽  
WeiGuo Zhang ◽  
XiLi Zhang
Keyword(s):  
Minimum Contrast Estimator ◽  
Minimum Contrast

scholarly journals A space-consistent version of the minimum-contrast estimator for linear stochastic evolution equations

2019 ◽  
Vol 20 (03) ◽  
pp. 2050019
Author(s):  
Pavel Kříž
Keyword(s):  
Evolution Equations ◽  
Index Formula ◽  
Spectral Approach ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Self Similarity ◽  
Fractional Noise ◽  
Minimum Contrast Estimator ◽  
Minimum Contrast ◽  
Drift Parameter

A new modification of the minimum-contrast estimator (the weighted MCE) of drift parameter in a linear stochastic evolution equation with additive fractional noise is introduced in the setting of the spectral approach (Fourier coordinates of the solution are observed). The reweighing technique, which utilizes the self-similarity property, achieves strong consistency and asymptotic normality of the estimator as number of coordinates increases and time horizon is fixed (the space consistency). In this respect, this modification outperforms the standard (non-weighted) MCE. Compared to other drift estimators studied within spectral approach (e.g., maximum likelihood, trajectory fitting), the weighted MCE is rather universal. It covers discrete time as well as continuous-time observations and it is applicable to processes with any value of Hurst index [Formula: see text]. To the author’s best knowledge, this is so far the first space-consistent estimator studied for [Formula: see text].

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