EFFICIENT ESTIMATION OF INTEGRATED VOLATILITY AND RELATED PROCESSES

2016 ◽  
Vol 33 (2) ◽  
pp. 439-478 ◽  
Author(s):  
Eric Renault ◽  
Cisil Sarisoy ◽  
Bas J.M. Werker
Keyword(s):  
Irregular Sampling ◽  
Efficient Estimation ◽  
Lower Efficiency ◽  
Sampling Schemes ◽  
Integrated Volatility ◽  
Nonparametric Bounds ◽  
Block Based ◽  
Power Variance ◽  
Nonparametric Efficiency ◽  
Observation Times

We derive nonparametric efficiency bounds for regular estimators of integrated smooth transformations of instantaneous variances, in particular, integrated power variance. We find that realized variance attains the efficiency bound for integrated variance under both regular and irregular sampling schemes. For estimating higher powers such as integrated quarticity, the block-based procedures of Mykland and Zhang (2009) can get arbitrarily close to the nonparametric bounds, when observation times are equidistant. Moreover, the estimator in Jacod and Rosenbaum (2013), whose efficiency was documented for the submodel assuming constant volatility, is efficient also for nonconstant volatility paths. When the observation times are possibly random but predictable, we provide an estimator, similar to that of Kristensen (2010), which can get arbitrarily close to the nonparametric bound. Finally, parametric information about the functional form of volatility leads to a lower efficiency bound, unless the volatility process is piecewise constant.

scholarly journals Bias correction for direct spectral estimation from irregularly sampled data including sampling schemes with correlation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nils Damaschke ◽  
Volker Kühn ◽  
Holger Nobach
Keyword(s):  
Spectral Estimation ◽  
Continuous Distribution ◽  
Discrete Distribution ◽  
Irregular Sampling ◽  
The Other ◽  
Sampled Data ◽  
Sampling Schemes ◽  
Other Hand ◽  
Sampling Intervals ◽  
Irregularly Sampled Data

AbstractThe prediction and correction of systematic errors in direct spectral estimation from irregularly sampled data taken from a stochastic process is investigated. Different sampling schemes are investigated, which lead to such an irregular sampling of the observed process. Both kinds of sampling schemes are considered, stochastic sampling with non-equidistant sampling intervals from a continuous distribution and, on the other hand, nominally equidistant sampling with missing individual samples yielding a discrete distribution of sampling intervals. For both distributions of sampling intervals, continuous and discrete, different sampling rules are investigated. On the one hand, purely random and independent sampling times are considered. This is given only in those cases, where the occurrence of one sample at a certain time has no influence on other samples in the sequence. This excludes any preferred delay intervals or external selection processes, which introduce correlations between the sampling instances. On the other hand, sampling schemes with interdependency and thus correlation between the individual sampling instances are investigated. This is given whenever the occurrence of one sample in any way influences further sampling instances, e.g., any recovery times after one instance, any preferences of sampling intervals including, e.g., sampling jitter or any external source with correlation influencing the validity of samples. A bias-free estimation of the spectral content of the observed random process from such irregularly sampled data is the goal of this investigation.

scholarly journals ASYMPTOTICALLY EFFICIENT ESTIMATION OF WEIGHTED AVERAGE DERIVATIVES WITH AN INTERVAL CENSORED VARIABLE

2016 ◽  
Vol 33 (5) ◽  
pp. 1218-1241 ◽  
Author(s):  
Hiroaki Kaido
Keyword(s):  
Support Function ◽  
Weighted Average ◽  
Interval Data ◽  
Efficient Estimation ◽  
Outcome Variable ◽  
Nonparametric Bounds ◽  
Regression Functions ◽  
Semiparametric Efficiency Bound ◽  
Derivatives Of ◽  
Interval Valued

This paper studies the identification and estimation of weighted average derivatives of conditional location functionals including conditional mean and conditional quantiles in settings where either the outcome variable or a regressor is interval-valued. Building on Manski and Tamer (2002, Econometrica 70(2), 519–546) who study nonparametric bounds for mean regression with interval data, we characterize the identified set of weighted average derivatives of regression functions. Since the weighted average derivatives do not rely on parametric specifications for the regression functions, the identified set is well-defined without any functional-form assumptions. Under general conditions, the identified set is compact and convex and hence admits characterization by its support function. Using this characterization, we derive the semiparametric efficiency bound of the support function when the outcome variable is interval-valued. Using mean regression as an example, we further demonstrate that the support function can be estimated in a regular manner by a computationally simple estimator and that the efficiency bound can be achieved.

Efficient estimation of integrated volatility incorporating trading information

2016 ◽  
Vol 195 (1) ◽  
pp. 33-50 ◽  
Author(s):  
Yingying Li ◽  
Shangyu Xie ◽  
Xinghua Zheng
Keyword(s):  
Efficient Estimation ◽  
Integrated Volatility

High-Frequency Observations: Identifiability and Asymptotic Efficiency

2014 ◽  
Author(s):  
Yacine Aïıt-Sahalia ◽  
Jean Jacod
Keyword(s):  
Statistical Models ◽  
Ad Hoc ◽  
Random Variable ◽  
Efficient Estimation ◽  
General Situation ◽  
Specific Reference ◽  
General Notion ◽  
Integrated Volatility ◽  
Classical Statistics ◽  
Definition Of

This chapter starts with a brief reminder about a number of concepts and results which pertain to classical statistical models, without specific reference to stochastic processes. It then introduces a general notion of identifiability for a parameter, in a semi-parametric setting. A parameter can be a number (or a vector), as in classical statistics; it can also be a random variable, such as the integrated volatility. The analysis is first conducted for Lévy processes, because in this case parameters are naturally non-random, and then extended to the more general situation of semimartingales. It also considers the problem of testing a hypothesis which is “random,” such as testing whether a discretely observed path is continuous or discontinuous: the null and alternative are not the usual disjoint subsets of a parameter space, but rather two disjoint subsets of the sample space, which leads to an ad hoc definition of the level, or asymptotic level, of a test in such a context. Finally, the chapter returns to the question of efficient estimation of a parameter, which is mainly analyzed from the viewpoint of “Fisher efficiency.”

scholarly journals Probe-corrected near-field to far-field transformation using multiple spherical wave expansions

2020 ◽  
Vol 12 (6) ◽  
pp. 447-454
Author(s):  
Fernando Rodríguez Varela ◽  
Belén Galocha Iragüen ◽  
Manuel Sierra Castañer
Keyword(s):  
Near Field ◽  
Spherical Wave ◽  
Irregular Sampling ◽  
Field Pattern ◽  
Far Field ◽  
Transformation Technique ◽  
Sampling Schemes ◽  
Field Transformation ◽  
Simulated Field ◽  
Far Field Pattern

AbstractNear-field to far-field transformations constitute a powerful antenna characterization technique for near-field measurement scenarios. In this paper, a near-field to far-field transformation technique based on multiple spherical wave expansions (SWEs) is presented. Thanks to its iterative matrix inversion nature, the approach performs the transformation of fields measured on arbitrary surfaces. Also, irregular sampling schemes can be incorporated. The proposed algorithm is based on modeling the antenna fields with not one, but several SWEs distributed over its geometry. Due to the high number of SWEs, their truncation number can be arbitrarily reduced. Working with expansions of low order allows us to incorporate the probe correction in the transformation in a very simple way, accepting any type of probe and orientation. Only the probe far-field pattern is used, thus working with its full SWE is avoided. The algorithm is validated using simulated field data as well as measurements of real antennas.

scholarly journals Efficient estimation of integrated volatility functionals via multiscale jackknife

2019 ◽  
Vol 47 (1) ◽  
pp. 156-176 ◽  
Author(s):  
Jia Li ◽  
Yunxiao Liu ◽  
Dacheng Xiu
Keyword(s):  
Efficient Estimation ◽  
Integrated Volatility
Sign in / Sign up

Export Citation Format

Share Document