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ARMA Representation of Integrated and Realized Variances

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  • Nour Meddahi

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Abstract

This paper derives the ARMA representation of integrated and realized variances when the spot variance depends linearly on two autoregressive factors, i.e., SR-SARV(2) models. This class of processes includes affine, GARCH diffusion, CEV models, as well as the eigenfunction stochastic volatility and the positive Ornstein-Uhlenbeck models. We also study the leverage effect case, the relationship between weak GARCH representation of returns and the ARMA representation of realized variances. Finally, various empirical implications of these ARMA representations are considered. We find that it is possible that some parameters of the ARMA representation are negative. Hence, the positiveness of the expected values of integrated or realized variances is not guaranteed. We also find that for some frequencies of observations, the continuous time model parameters may be weakly or not identified through the ARMA representation of realized variances. Nous dérivons la représentation ARMA des variances intégrées et réalisées quand la variance instantanée est la combinaison linéaire de deux facteurs auto-régressifs, c'est-à-dire, les modèles SR-SARV(2). Cette classe de processus contient les modèles affines, diffusion GARCH, CEV, à fonctions propres, ainsi que les processus Ornstein-Uhlenbeck et positifs. Nous étudions le cas à effet de levier, et aussi le lien entre la représentation GARCH faible des rendements et la représentation ARMA de la volatilité réalisée. Finalement, nous analysons les conséquences empiriques de ces représentations ARMA. Nous trouvons qu'il est possible que certains paramètres de la représentation ARMA soient négatifs. Ainsi, la positivité de l'espérance linéaire des variances intégrées et réalisées n'est pas assurée. Nous trouvons aussi que pour certaines fréquences d'observation, les paramètres du modèle en temps continu peuvent être faiblement identifiables ou pas identifiables à partir de la représentation ARMA de variances réalisées.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2002s-93.

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Date of creation: 01 Dec 2002
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Handle: RePEc:cir:cirwor:2002s-93

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Keywords: Integrated variance; realized variance; ARMA representation; SR-SARV models; weak identification; variance intégrée; variance réalisée; représentation ARMA; modèles SR-SARV; faible identification;

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