Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps

By Mark Podolskij, Mathias Vetter. 2007

302 citations recorded by the source corpus.

We propose a new concept of modulated bipower variation for diffusion models with microstructure noise. We show that this method provides simple estimates for such important quantities as integrated volatility or integrated quarticity. Under mild conditions the consistency of modulated bipower variation is proven. Under further assumptions we prove stable convergence of our estimates with the optimal rate n^(-1/4). Moreover, we construct estimates which are robust to finite activity jumps.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/34a1936544f7af5a42fb3eff49cb7dc01609e063

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Citations in the corpus

Microstructure Noise in the Continuous Case: The Pre-Averaging Approach ∗ (2008, methodology): “The purpose of this paper is to give more insight to the third approach of pre-averaging, which was introduced in Podolskij and Vetter (2006).”
High-Frequency Jump Analysis of the Bitcoin Market* (2017, methodology): “traders are responsible for most of the transactions. • P i is the median observed price. • RV i is the realized variance of the latent price during the period, given by the noise-robust estimator of Podolskij and Vetter (2009). • NV i is the variance of the microstructure noise, estimated as in Lee”
Limit theorems for moving averages of discretized processes plus noise (2010, methodology): “It is done in the context of the ”preaveraging method” developed in [11] and [13] for the estimation of the integrated volatility for a continuous semimartingale.”
Pre-Averaging Estimators of the Ex-Post Covariance Matrix in Noisy Diffusion Models with Non-Synchronous Data (2010, unknown): “Now, recall that ∆ n k i X k can be replaced with ( σ s ∆ n k i W ) k for any s with t without changing the ﬁrst-order asymptotics (see, e.g., Podolskij and Vetter, 2009).”
An estimator for the quadratic covariation of asynchronously observed Itô processes with noise: Asymptotic distribution theory (2011, methodology): “A refinement of the subsample approach using multiple scales in [30] and related alternative techniques in [4], [23] and [29] have led to rate-optimal estimators and feasible stable central limit theorems.”
Rough Volatility: Fact or Artefact? (2022, background): “Several empirical studies have attempted to estimate the roughness of ‘realized volatility’ signals using high-frequency data [1, 3, 11, 19, 24].”
Estimation of continuous-time stochastic volatility models with jumps using high-frequency data (2009, methodology): “By extending the analysis of Podolskij and Vetter (2007)(14), it should be possible to prove also that B̃V δ(t) and T̃ V δ(t) converge to IV (t) at rate δ.”
Asymptotic equivalence for inference on the volatility from noisy observations (2011, methodology): “Podolskij and Vetter (2009) use Haar functions as Φk (they were aware of the fact that discretized sine functions would slightly increase the Fisher information), but they have not used higher frequencies j.”
Jump detection with wavelets for high-frequency financial time series (2014, methodology): “Our method to estimate the volatility is consistent with the ‘pre-averaging’ method proposed and developed by Podolskij and Vetter (2009) and Jacod et al. (2009).”
MODELING HIGH-FREQUENCY FINANCIAL DATA BY PURE JUMP PROCESSES (2012, methodology): “See, for example, Aı̈t-Sahalia, Mykland and Zhang (2005), Zhang, Mykland and Aı̈t-Sahalia (2005), Zhang (2006), Fan and Wang (2007), Podolskij and Vetter (2009) and Jacod et al. (2009), among others.”
Realised quantile-based estimation of the integrated variance (2010, methodology): “By the same methods as presented in Podolskij and Vetter (2007) we can show that N ( QRV ∗ N (m,λ, α)− 3 c2 ω̂(2) − IV ) = N ( M(p) + N(p) + C(p) ) + γN (p) , (64)”
A Note on the Central Limit Theorem for Bipower Variation of General Functions. (2008, background): “…(see Barndorff-Nielsen & Shephard (2006), Christensen & Podolskij (2006b) or Ait-Sahalia & Jacod (2006)) or to provide goodness-of-fit tests for the parametric form of the volatility function in stochastic differential equations (see Dette, Podolskij & Vetter (2006) or Dette & Podolskij (2006)).”
Variance Dynamics: Joint Evidence from Options and High-Frequency Returns (2011, methodology): “To measure the statistical significance of the performance difference, I construct a likelihood ratio test for non-nestedmodels according to Vuong (1989), Vpc = √ N − 1μlr/σlr , where μlr and σlr denote the sample mean and standard deviation of the daily likelihood ratios between the two models p an”