Efficient estimation of integrated volatility and related processes

E. Renault, Cisil Sarisoy, Bas Werker

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We derive nonparametric bounds for inference about functionals of high-frequency volatility, in particular, integrated power variance. In the absence of microstructure noise, we find that standard Realized Variance attains the nonparametric efficiency bound, also in case of unequally spaced random observation times. For higher powers, e.g., integrated quarticity, the block-based procedures of Mykland and Zhang (2009) can get arbitrarily close to the nonparametric bounds in case of equally spaced observations. The estimator in Jacod and Rosenbaum (2013) is efficient, also at non-constant volatility, still for equally spaced data. For unequally spaced data, we provide an estimator, similar to that of Kristensen (2010), that can get arbitrarily close to the nonparametric bound. Finally, contrary to public opinion, we demonstrate that parametric information about the functional form of volatility generally leads to a decreased lower bound, unless the volatility process is piecewise constant.
Original languageEnglish
Pages (from-to)439-478
JournalEconometric Theory
Volume33
Issue number2
DOIs
Publication statusPublished - Apr 2017

Fingerprint

public opinion
efficiency
Efficient estimation
Integrated volatility
Nonparametric bounds
time
Integrated
Estimator
Public opinion
Efficiency bounds
Realized variance
Microstructure noise
Inference
Functional form
Lower bounds

Keywords

  • High-frequency data
  • Integrated power variance
  • Local Asymptotic Normality
  • Nonparametric efficiency bounds
  • Realized volatility
  • Volatility estimation

Cite this

Renault, E. ; Sarisoy, Cisil ; Werker, Bas. / Efficient estimation of integrated volatility and related processes. In: Econometric Theory. 2017 ; Vol. 33, No. 2. pp. 439-478.
@article{c15660705e3a489db63e1ecf2b9f7082,
title = "Efficient estimation of integrated volatility and related processes",
abstract = "We derive nonparametric bounds for inference about functionals of high-frequency volatility, in particular, integrated power variance. In the absence of microstructure noise, we find that standard Realized Variance attains the nonparametric efficiency bound, also in case of unequally spaced random observation times. For higher powers, e.g., integrated quarticity, the block-based procedures of Mykland and Zhang (2009) can get arbitrarily close to the nonparametric bounds in case of equally spaced observations. The estimator in Jacod and Rosenbaum (2013) is efficient, also at non-constant volatility, still for equally spaced data. For unequally spaced data, we provide an estimator, similar to that of Kristensen (2010), that can get arbitrarily close to the nonparametric bound. Finally, contrary to public opinion, we demonstrate that parametric information about the functional form of volatility generally leads to a decreased lower bound, unless the volatility process is piecewise constant.",
keywords = "High-frequency data, Integrated power variance, Local Asymptotic Normality, Nonparametric efficiency bounds, Realized volatility, Volatility estimation",
author = "E. Renault and Cisil Sarisoy and Bas Werker",
year = "2017",
month = "4",
doi = "10.1017/S0266466616000013",
language = "English",
volume = "33",
pages = "439--478",
journal = "Econometric Theory",
issn = "0266-4666",
publisher = "CAMBRIDGE UNIV PRESS",
number = "2",

}

Efficient estimation of integrated volatility and related processes. / Renault, E.; Sarisoy, Cisil; Werker, Bas.

In: Econometric Theory, Vol. 33, No. 2, 04.2017, p. 439-478.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Efficient estimation of integrated volatility and related processes

AU - Renault, E.

AU - Sarisoy, Cisil

AU - Werker, Bas

PY - 2017/4

Y1 - 2017/4

N2 - We derive nonparametric bounds for inference about functionals of high-frequency volatility, in particular, integrated power variance. In the absence of microstructure noise, we find that standard Realized Variance attains the nonparametric efficiency bound, also in case of unequally spaced random observation times. For higher powers, e.g., integrated quarticity, the block-based procedures of Mykland and Zhang (2009) can get arbitrarily close to the nonparametric bounds in case of equally spaced observations. The estimator in Jacod and Rosenbaum (2013) is efficient, also at non-constant volatility, still for equally spaced data. For unequally spaced data, we provide an estimator, similar to that of Kristensen (2010), that can get arbitrarily close to the nonparametric bound. Finally, contrary to public opinion, we demonstrate that parametric information about the functional form of volatility generally leads to a decreased lower bound, unless the volatility process is piecewise constant.

AB - We derive nonparametric bounds for inference about functionals of high-frequency volatility, in particular, integrated power variance. In the absence of microstructure noise, we find that standard Realized Variance attains the nonparametric efficiency bound, also in case of unequally spaced random observation times. For higher powers, e.g., integrated quarticity, the block-based procedures of Mykland and Zhang (2009) can get arbitrarily close to the nonparametric bounds in case of equally spaced observations. The estimator in Jacod and Rosenbaum (2013) is efficient, also at non-constant volatility, still for equally spaced data. For unequally spaced data, we provide an estimator, similar to that of Kristensen (2010), that can get arbitrarily close to the nonparametric bound. Finally, contrary to public opinion, we demonstrate that parametric information about the functional form of volatility generally leads to a decreased lower bound, unless the volatility process is piecewise constant.

KW - High-frequency data

KW - Integrated power variance

KW - Local Asymptotic Normality

KW - Nonparametric efficiency bounds

KW - Realized volatility

KW - Volatility estimation

U2 - 10.1017/S0266466616000013

DO - 10.1017/S0266466616000013

M3 - Article

VL - 33

SP - 439

EP - 478

JO - Econometric Theory

JF - Econometric Theory

SN - 0266-4666

IS - 2

ER -