Semiparametric Estimation in Continuous-Time: Asymptotics for Integrated Volatility Functionals With Small and Large Bandwidths

Yang, Xiye

doi:10.2139/ssrn.3243457

Cited by 5 publications

(4 citation statements)

References 42 publications

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“…This is the commonly used estimator for integrated volatility functionals, which has been studied intensively in the literature (see, e.g., Rosenbaum (2013, 2015), Li et al (2019), and Yang (2021) among others). Since we only need a consistent variance estimator here, one does not have to correct for the asymptotic bias of such a plug-in estimator (although the bias-corrected estimator may have better finite sample performance).…”

Section: A2 Variance Estimatorsmentioning

confidence: 99%

Estimation of Leverage Effect: Kernel Function and Efficiency

Yang

2022

Journal of Business & Economic Statistics

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Section: A2 Variance Estimatorsmentioning

confidence: 99%

Estimation of Leverage Effect: Kernel Function and Efficiency

Yang

2022

Journal of Business & Economic Statistics

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“…In view of these results, we keep both B NL n and B ANB n in our analysis. In a different setup with the non-stationary underlying process and in-fill asymptotics, Yang (2018) adopts a similar approach. The following theorem gives the first main result of this paper.…”

Section: Example (Kernel Density Estimator Continued)mentioning

confidence: 99%

“…It might happen that the bias B ANB n is identically zero. For example, in the continuous-time setting (with in-fill asymptotics), Yang (2018) has shown that, when estimating integrated volatility functionals, the counterpart of B ANB n , which is the first-order effect of the nonparametric bias, is canceled by the discretization error. In the cited paper, what left is the counterpart of the following second-order effect of the nonparametric bias:…”

Section: Example (Kernel Density Estimator Continued)mentioning

confidence: 99%

Bias Correction and Robust Inference in Semiparametric Models

Choi

Yang

2019

SSRN Journal

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This paper analyzes several different biases that emerge from the (possibly) low-precision nonparametric ingredient in a semiparametric model. We show that both the variance part and the bias part of the nonparametric ingredient can lead to some biases in the semiparametric estimator, under conditions weaker than typically required in the literature. We then propose two biasrobust inference procedures, based on multi-scale jackknife and analytical bias correction, respectively. We also extend our framework to the case where the semiparametric estimator is constructed by some discontinuous functionals of the nonparametric ingredient. The simulation study shows that both biascorrection methods have good finite-sample performance.

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“…Recently, Li et al (2019) introduced jackknife for bias correction and a simulation-based method for variance estimation, which are derivative-free and greatly facilitate applications. Li and Liu (2017) studied efficient functional estimation when volatility exhibits longmemory property, Yang (2018) utilized matrix calculus to ease the burden of computing derivatives and removed various bias terms to allow a more flexible range of the tuning parameter. More recently, Chen (2019) uses pre-averaging method to provide noise-robust and rate-optimal functional estimators and extends the inferential theory of volatility functionals to the setting of noisy data.…”

Section: Introductionmentioning

confidence: 99%

The Fourier Transform Method for Volatility Functional Inference by Asynchronous Observations

Chen

2019

Preprint

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We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time alignment nor data imputation. Under conditions, this spectral approach is consistent and we provide limit distributions using irregular and asynchronous observations. When observations are synchronous, the Fourier transform method for volatility functionals attains both the optimal convergence rate and the efficient bound in the sense of Le Cam and Hájek. Another finding is asynchronicity or missing data as a form of noise produces "interference" in the spectrum estimation and impacts on the convergence rate of volatility functional estimators. This new methodology extends previous applications of volatility functionals, including principal component analysis, generalized method of moments, continuous-time linear regression models et cetera, to high-frequency datasets of which asynchronicity is a prevailing feature.

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Semiparametric Estimation in Continuous-Time: Asymptotics for Integrated Volatility Functionals With Small and Large Bandwidths

Cited by 5 publications

References 42 publications

Estimation of Leverage Effect: Kernel Function and Efficiency

Estimation of Leverage Effect: Kernel Function and Efficiency

Bias Correction and Robust Inference in Semiparametric Models

The Fourier Transform Method for Volatility Functional Inference by Asynchronous Observations

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