Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Irregular sampling and central limit theorems for power variations: The continuous case

Takaki Hayashi, Jean Jacod, and Nakahiro Yoshida

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Abstract

In the context of high frequency data, one often has to deal with observations occurring at irregularly spaced times, at transaction times for example in finance. Here we examine how the estimation of the squared or other powers of the volatility is affected by irregularly spaced data. The emphasis is on the kind of assumptions on the sampling scheme which allow to provide consistent estimators, together with an associated central limit theorem, and especially when the sampling scheme depends on the observed process itself.

Résumé

Dans le contexte de données à haute fréquences, il est fréquent de recueillir les informations le long d’une grille irrégilière, par exemple aux instants de transaction pour les données financières. Dans cet article, nous étudions comment l’estimation de l’intégrale du carré, ou d’autres puissances, de la volatilité est affectée par l’irrégularité des données. L’accent est mis sur le type d’hypothèses qu’il est nécessaire de faire sur la répartition des observations, en particulier lorsque celles-ci dépendent du processus observé lui-même, de façon à obtenir un théorème limite central pour nos estimateurs.

Article information

Source
Ann. Inst. H. Poincaré Probab. Statist., Volume 47, Number 4 (2011), 1197-1218.

Dates
First available in Project Euclid: 6 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1317906508

Digital Object Identifier
doi:10.1214/11-AIHP432

Mathematical Reviews number (MathSciNet)
MR2884231

Zentralblatt MATH identifier
1271.62198

Subjects
Primary: 60G44: Martingales with continuous parameter 62M09: Non-Markovian processes: estimation
Secondary: 60G42: Martingales with discrete parameter 62G20: Asymptotic properties

Keywords
Quadratic variation Discrete observations Power variations High frequency data Stable convergence

Citation

Hayashi, Takaki; Jacod, Jean; Yoshida, Nakahiro. Irregular sampling and central limit theorems for power variations: The continuous case. Ann. Inst. H. Poincaré Probab. Statist. 47 (2011), no. 4, 1197--1218. doi:10.1214/11-AIHP432. https://projecteuclid.org/euclid.aihp/1317906508


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