Discretization of Processes

Jacod, Jean; Protter, Philip

doi:10.1007/978-3-642-24127-7

Cited by 327 publications

(536 citation statements)

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“…Assumption A imposes very mild regularities on the process X and is standard in the literature on discretized processes; see Jacod and Protter (2012). The dominance condition in Assumption A is only required to hold locally in time up to the stopping time T m , which often take forms of hitting times of adapted processes; this requirement is much weaker than a global dominance condition that corresponds to T m ≡ +∞.…”

Section: The Underlying Processmentioning

confidence: 99%

“…The dominance condition in Assumption A is only required to hold locally in time up to the stopping time T m , which often take forms of hitting times of adapted processes; this requirement is much weaker than a global dominance condition that corresponds to T m ≡ +∞. This more general setup, however, does not add any technical complexity into our proofs, thanks to the standard localization procedure in stochastic calculus; see Section 4.4.1 in Jacod and Protter (2012) for a review on the localization procedure.…”

Section: The Underlying Processmentioning

confidence: 99%

“…Finally, we show (A.6). When r ∈ (0, 1], by Assumption SA and Lemma 2.1.7 in Jacod and Protter (2012),…”

Section: A11 Estimates For the Kernel (R X)mentioning

confidence: 99%

“…In this paper we focus attention on the diffusive volatility part of X while recognizing the presence of jumps in X . Most of the existing literature has concentrated on estimating nonparametrically volatility functionals of the form T 0 g(V s )ds for some smooth function g, typically three times continuously differentiable (see, e.g., Andersen et al (2013), Renault et al (2014), Jacod and Protter (2012), Jacod and Rosenbaum (2013) and many references therein). The most important example is the integrated variance T 0 V s ds, which is widely used in empirical work.…”

Section: Introductionmentioning

confidence: 99%

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Estimating the Volatility Occupation Time via Regularized Laplace Inversion

Jia

Todorov²,

Tauchen

2015

Econom. Theory

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We propose a consistent functional estimator for the occupation time of the spot variance of an asset price observed at discrete times on a finite interval with the mesh of the observation grid shrinking to zero. The asset price is modeled nonparametrically as a continuous-time Itô semimartingale with nonvanishing diffusion coefficient. The estimation procedure contains two steps. In the first step we estimate the Laplace transform of the volatility occupation time and, in the second step, we conduct a regularized Laplace inversion. Monte Carlo evidence suggests that the proposed estimator has good small-sample performance and in particular it is far better at estimating lower volatility quantiles and the volatility median than a direct estimator formed from the empirical cumulative distribution function of local spot volatility estimates. An empirical application shows the use of the developed techniques for nonparametric analysis of variation of volatility.

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Section: The Underlying Processmentioning

confidence: 99%

Section: The Underlying Processmentioning

confidence: 99%

“…Finally, we show (A.6). When r ∈ (0, 1], by Assumption SA and Lemma 2.1.7 in Jacod and Protter (2012),…”

Section: A11 Estimates For the Kernel (R X)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Estimating the Volatility Occupation Time via Regularized Laplace Inversion

Jia

Todorov²,

Tauchen

2015

Econom. Theory

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“…For this reason, the development of statistical tools modeled by discretely observed Itō semimartingales has been a major topic over the last years, both regarding the estimation of crucial quantities used for model calibration purposes and with a view on tests to check whether a certain model fits the data well. For a detailed overview of the 1 state of the art we refer to the recent monographs by Jacod and Protter (2012) and Aït-Sahalia and Jacod (2014). These statistical tools typically differ highly, depending on the quantities of interest.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric inference of gradual changes in the jump behaviour of time-continuous processes

Hoffmann

Vetter

Dette

2018

Stochastic Processes and their Applications

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In applications changes of the properties of a stochastic feature occur often gradually rather than abruptly, that is: after a constant phase for some time they slowly start to change. Efficient analysis for change points should address the specific features of such a smooth change. In this paper we discuss statistical inference for localizing and detecting gradual changes in the jump characteristic of a discretely observed Itō semimartingale. We propose a new measure of time variation for the jump behaviour of the process. The statistical uncertainty of a corresponding estimate is analyzed deriving new results on the weak convergence of a sequential empirical tail integral process and a corresponding multiplier bootstrap procedure.

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