Discretization of Processes

By Jean Jacod, Philip Protter. 2011

439 citations recorded by the source corpus.

Subfields: Computational Mechanics, Management, Monitoring, Policy and Law, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/57fea254d7d0654c93adf775bc8476520f7b342c

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In Computational Mechanics

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Citations in the corpus

Time-Varying Periodicity in Intraday Volatility (2019, background): “This situation mirrors some features of the CLT for measuring quantities associated with the jump part of X, such as their quadratic variation, see, for example, Jacod and Protter (2012).”
Estimation of integrated volatility of volatility with applications to goodness-of-fit testing (2011, methodology): “Such problems have been solved for the price process X in recent years (see [18] for an overview), and in principle the methods are all based on the estimation of plain integrated volatility ∫ t 0 σ(2) s ds and further quantities, such as truncated versions or bipower variation.”
Volatility estimation for stochastic PDEs using high-frequency observations (2017, background): “Considering discrete high-frequency data in time, our aim is to extend the well understood statistical theory for semi-martingales, see, for instance, Jacod and Protter (2012), Mykland and Zhang (2009) or Jacod and Rosenbaum (2013), to parabolic SPDEs whose solution can be understood as infinite dim”
Is the diurnal pattern sufficient to explain intraday variation in volatility? A nonparametric assessment (2017, positive): “…enlarge the feasible set of powers for which we can do hypothesis testing, we follow Corsi, Pirino, and Ren`o (2010) in the no-noise and finite-activity jump setting by combining the bipower idea with the truncation approach of Mancini (2009); Jacod and Protter (2012); Jing, Liu, and Kong (2014).”
High-frequency factor models and regressions (2020, positive): “, Jacod and Protter (2012). Next, we construct an OLS estimator of β̂i∆n based on Equation (10), β̂i∆n = (X T i Xi) −1X T i Yi.”
High-frequency analysis of parabolic stochastic PDEs (2018, background): “Examples of volatility models for σ(1) include Ornstein–Uhlenbeck processes in space and time (see [5, 36]) and their generalizations (see [12, 43]).”
A remark on the rates of convergence for integrated volatility estimation in the presence of jumps (2012, methodology): “mates, which follow from the property Ft({x:|x|>1})≤Aand from the fact that if ∆n i Z6=0 there is at least one jump of Zwithin the interval (i−1 n , i n] (this estimate follows from Lemma 2.1.7 of [4] applied to the counting process P s≤t 1{∆Zs6=0 }): P(∆n i Z6=0) ≤ K n (4.12) . 12 J. JACOD AND M”
Principal Component Analysis of High-Frequency Data (2016, methodology): “Nevertheless, it is possible to construct a “PCA” procedure on the integrated covariance matrix, whose asymptotic results are immediately available by applying the “delta” method, using Lemma 2 and Theorem 13.2.4 in Jacod and Protter (2012).”
Adaptive estimation of continuous-time regression models using high-frequency data (2017, methodology): “The estimation of S(g) is done via the general block-based method of Jacod and Rosenbaum (2013), see also Jacod and Protter (2012).”
Roughing up Beta: Continuous vs. Discontinuous Betas, and the Cross-Section of Expected Stock Returns (2014, neutral): “For the diffusive part, in particular, this entails no assumptions and follows merely from the partition of a correlated bivariate Brownian motion into its orthogonal components (see, e.g., Theorem 2.1.2 in Jacod and Protter, 2012).”
Time-changed CIR default intensities with two-sided mean-reverting jumps (2014, neutral): “This form of Itô’s formula based on characteristics can be found in Jacod and Protter (2011), equation (2.1.20), page 32.”
Rough Volatility: Fact or Artefact? (2022, neutral): “This estimation error is far from i.i.d.: it is known to possess path-dependent features (see Jacod and Protter, 2012).”