A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales

By Ole E. Barndorff-Nielsen, S. Graversen, Jean Jacod, Mark Podolskij, N. Shephard. 2004

270 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/69893e15a88a6eb55e82ae47ee8b65d2126aa99c

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Citations in the corpus

A remark on the rates of convergence for integrated volatility estimation in the presence of jumps (2012, background): “omeknownresults. We consider a one-dimensional Itˆo semimartingale Xon a ﬁltered space (Ω,F,(Ft)t≥0,P), which is observed at regularly spaced times i n for i=0,1,...,n, over the (ﬁxed) ﬁnite interval [0,1]. The characteristics (B,C,ν) where Bis the drift, Cthe integrated volatility and RATES FOR INT”
Pre-Averaging Estimators of the Ex-Post Covariance Matrix in Noisy Diffusion Models with Non-Synchronous Data (2010, unknown): “In independent and concurrent work to ours, Barndorff-Nielsen et al. (2008b) propose a multivariate realised kernel.”
Econometric analysis of jump-driven stochastic volatility models (2011, background): “and Shephard (2004), Barndorfi-Nielsen, Shephard, and Winkel (2005) and Woerner (2002)”
Power variation of some integral fractional processes (2006, result): “Refinements of their results have been obtained in Woerner (2003, 2005), and further extensions can be found in Barndorff-Nielsen et al. (2006).”
Semi-Parametric Comparison of Stochastic Volatility Models using Realized Measures (2006, background): “It may seem a little surprising that, although Barndorff-Nielsen et al. (2006) have shown that √ M Nt,M is asymptotically mixed normal, as in the case of realized volatility, Assumption 1 holds only with bM = O(M1/2).”
Asymptotic analysis of hedging errors in models with jumps (2009, background): “A related problem arises in the context of asymptotic behavior of realized volatility and power variation [1,2,13].”
Limit theorems for moving averages of discretized processes plus noise (2010, unknown): “See, for instance, [4] or [10] among others.”
Limit Theorems for Power Variations of Pure-Jump Processes with Application to Activity Estimation (2011, methodology): “Second if M is a continuous martingale orthogonal to the Brownian motion Wt used in defining σt, we can proceed similar to Barndorff-Nielsen et al. (2005) and argue as follows. If we set Nt = E (|∆i X(τ)||Ft) for t ≥ (i− 1)∆n, then (Nt)t≥(i−1)∆n is a martingale. It remains also martingale, condition”
Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data (2011, methodology): “and Bez and Bertrand (2011), who argued that the critical relationship (4) between the fractal index of a stochastic process whose variogram of order p > 0 shows a behavior of the form (5) at the origin, and the fractal dimension of its sample paths, is particularly robust and inclusive when p= 1. W”
Limit theorems for multipower variation in the presence of jumps (2006, background): “[1], to reveal integrated volatility powers in general Brownian semimartingales.”
On the Estimation of Integrated Volatility With Jumps and Microstructure Noise (2014, methodology): “Finally, (A.10) follows from a standard procedure of Riemann integrability (see Barndorff-Nielsen et al. 2006).”
A Note on the Central Limit Theorem for Bipower Variation of General Functions. (2008, unknown): “μi (6) = 1 √ n E [( ∇g(γ̄ i ) −∇g(β i ) )(√ n∆i X − β i ) h(β n i )|F i−1 n ]”
Bipower-type estimation in a noisy diffusion setting (2008, methodology): “[4] shows that the proof of this claim works in the same way, provided one uses assumption (A) in two 29”