Quarticity and other functionals of volatility: Efficient estimation

Jacod, Jean; Rosenbaum, Mathieu

doi:10.1214/13-aos1115

Cited by 123 publications

(140 citation statements)

References 16 publications

(21 reference statements)

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“…Lemma A1, below, collects some known, but nontrivial, estimates from Jacod and Rosenbaum (2013); see (4.8), (4.11), (4.12), Lemma 4.2, and Lemma 4.3 in that paper.…”

Section: Assumption A1mentioning

confidence: 99%

Generalized Method of Integrated Moments for High-Frequency Data

Jia

Xiu

2016

Econometrica

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We propose a semiparametric two‐step inference procedure for a finite‐dimensional parameter based on moment conditions constructed from high‐frequency data. The population moment conditions take the form of temporally integrated functionals of state‐variable processes that include the latent stochastic volatility process of an asset. In the first step, we nonparametrically recover the volatility path from high‐frequency asset returns. The nonparametric volatility estimator is then used to form sample moment functions in the second‐step GMM estimation, which requires the correction of a high‐order nonlinearity bias from the first step. We show that the proposed estimator is consistent and asymptotically mixed Gaussian and propose a consistent estimator for the conditional asymptotic variance. We also construct a Bierens‐type consistent specification test. These infill asymptotic results are based on a novel empirical‐process‐type theory for general integrated functionals of noisy semimartingale processes.

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“…Lemma A1, below, collects some known, but nontrivial, estimates from Jacod and Rosenbaum (2013); see (4.8), (4.11), (4.12), Lemma 4.2, and Lemma 4.3 in that paper.…”

Section: Assumption A1mentioning

confidence: 99%

Generalized Method of Integrated Moments for High-Frequency Data

Jia

Xiu

2016

Econometrica

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“…However, the bounds might not be sharp. Efficiency issues in the estimation of integrated volatility functionals of the form T 0 g(V s )ds has recently been tackled by Jacod and Reiß (2014), Jacod and Rosenbaum (2013) and Renault et al (2014) for smooth g(·). The VOT, on the other hand, corresponds to a discontinuous transform g(·) = 1 {·≤x} .…”

Section: Suppose (I) There Exist a Localizing Sequence (T M ) M≥1 Omentioning

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%

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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“…where g is smooth (e.g., Barndorff-Nielsen, Graversen, Jacod, Podolskij, and Shephard, 2006;Jacod and Rosenbaum, 2013). Here, in contrast, g is discontinuous, which makes the theory a lot more inaccessible.…”

Section: A Discrete and Noisy High-frequency Record Of Xmentioning

confidence: 99%