Limit theorems for moving averages of discretized processes plus noise

By Jean Jacod, Mark Podolskij, Mathias Vetter. 2010

112 citations recorded by the source corpus.

This paper presents some limit theorems for certain functionals of moving averages of semi-martingales plus noise, which are observed at high frequency. Our method generalizes the pre-averaging approach (see [13],[11]) and provides consistent estimates for various characteristics of general semi-martingales. Furthermore, we prove the associated multidimensional (stable) central limit theorems. As expected, we find central limit theorems with a convergence rate n1=4, if n is the number of observations.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/8c91c23f60e810e7784f265e7f495e5124acfce9

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In Management Science and Operations Research

Citations in the corpus

Preaveraging-Based Estimation of Quadratic Variation in the Presence of Noise and Jumps: Theory, Implementation, and Empirical Evidence (2013, background): “Applying theorem 3.3 from Jacod, Podolskij, and Vetter (2009) for p = 2,4 (which is also valid for the q-dependent noise), we deduce that 1−p/4n [t/ n]−kn∑ i=0 ∣∣Zni ∣∣p P−→ mp ∫ t 0 ( θψ2σ 2 u + θ−1ψ1ρ2 )p/2 du, where mp = E[|N (0, 1)|p].”
On the Estimation of Integrated Volatility With Jumps and Microstructure Noise (2014, methodology): “For more detailed discussion about the new probability space, see, Jacod, Podolskij, and Vetter (2010).”
Testing for jumps in noisy high frequency data (2012, methodology): “…estimation: maximum likelihood estimation (Aït-Sahalia et al., 2005; Xiu, 2010), linear combination of realized volatilities obtained by subsampling (Zhang et al., 2005; Zhang, 2006), linear combination of autocovariances (Barndorff-Nielsen et al., 2008) and preaveraging (Jacod et al., 2009, 2010).”
Is the diurnal pattern sufficient to explain intraday variation in volatility? A nonparametric assessment (2017, unknown): “In particular, in Corollary 4.1, if all the powers are even numbers (e.g., l 1 = 4 , r 1 = 0 , l 2 = 2 and r 2 = 0 ), we can prove the results in the general setting of Jacod, Podolskij, and Vetter (2010) with heteroskedastic noise, which is of a general form Here, the null is modified as Note.”