Bipower Variation for Gaussian Processes with Stationary Increments

By Ole E. Barndorff-Nielsen, José Manuel Corcuera, Mark Podolskij, Jeannette H. C. Woerner. Journal of Applied Probability, 2009

99 citations recorded by the source corpus.

Subfields: Finance, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/81db23c73a3117c74e07e9e773ce52bac1880e7a

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Citations in the corpus

Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data (2011, methodology): “This approach can be paired with the use of trimmed means or linear combinations of sample quantiles in defining power variations, as suggested by Coeurjolly (2008) for time series, or with the use of bipower and multipower variations (Barndorff-Nielsen et al. 2006; Barndorff-Nielsen, Corcuera and P”
Multipower Variation for Brownian Semistationary Processes (2011, methodology): “These assumptions were proposed by Guyon and Leon in [22] (those authors considered the case of centered, stationary Gaussian processes X ; this relates to the BSS setting with σ constant) and the same assumptions were used in [3] and [5].”
Stein’s method on Wiener chaos (2007, background): “Remark 3.4 Theorem 3.3 and its generalizations have been applied to a variety of frameworks, such as: p-variations of stochastic integrals with respect to Gaussian processes [ 2 , 12], quadratic functionals of bivariate Gaussian processes [14], self-intersection local times of fractional Brownian mo”
Volatility estimation for stochastic PDEs using high-frequency observations (2017, methodology): “Barndorff-Nielsen et al. (2009) and related works provide a stable limit theorem for power variations of stochastic integrals with respect to general Gaussian processes. However, it does also not apply to our model based on the spectral decomposition (6). Instead, we exploit the decay of the autocov”
New Berry-Esseen bounds for non-linear functionals of Poisson random measures (2013, background): “asure or with functionals of a Poisson random measure. Applications of ﬁndings dealing with the Gaussian case have found notable applications in the theory and statistics of Gaussian random processes [3, 4] (most prominently the fractional Brownian motion [15]), spherical random ﬁelds [1, 14], rando”
Limit Theorems for Functionals of Higher Order Differences of Brownian Semi-Stationary Processes (2009, unknown): “(An extension to other integral processes) In [4] and [5] we considered processes of the form Zt = μ+ ∫ t”
Quantitative Breuer-Major Theorems (2010, unknown): “…(recent) sample: renormalization of fractional diﬀusions [1], power variations of Gaussian and Gaussian-related continuous-time processes [3, 4, 15, 21], Gaussian ﬂuctuations of heat-type equations [5], estimation of Hurst parameters of fractional processes [9, 13, 14], unit root…”