Irregular sampling and central limit theorems for power variations : the continuous case
Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) no. 4, pp. 1197-1218.

Dans le contexte de données à haute fréquences, il est fréquent de recueillir les informations le long d'une grille irrégulière, 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.

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.

DOI : 10.1214/11-AIHP432
Classification : 60G44, 62M09, 60G42, 62G20
Mots-clés : quadratic variation, discrete observations, power variations, high frequency data, stable convergence 
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Hayashi, Takaki; Jacod, Jean; Yoshida, Nakahiro. Irregular sampling and central limit theorems for power variations : the continuous case. Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) no. 4, pp. 1197-1218. doi : 10.1214/11-AIHP432. http://archive.numdam.org/articles/10.1214/11-AIHP432/

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