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ARMA Representation of Two-Factor Models

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Nour Meddahi ()
Abstract

Many financial time series models are specified through a structural representation. Nonetheless, knowing their reduced ARMA form may be useful for impulse response analysis, filtering, forecasting, and for purposes of statistical inference. This ARMA representation is the analytical steady-state of the unobservable variable and is therefore an alternative approach to Kalman filter-based methods. In this paper, we analytically derive the moving-average roots of a two-factor model. We then provide a financial application. More precisely, we characterize the weak GARCH(2,2) representation of continuous time stochastic volatility models when the variance process is a linear combination of two autoregressive processes, as in affine, GARCH diffusion, CEV, positive Ornstein-Uhlenbeck, eigenfunction, and SR-SARV processes.

Beaucoup de modèles financiers sont spécifiés à travers des représentations structurelles. Néanmoins, la connaissance de formes réduites ARMA peut être utile pour l'analyse de fonction de réponses, le filtrage, la prévision, et pour les méthodes d'inférence statistique. Cette représentation ARMA est la forme analytique de l'état stable de la variable inobservable et est donc une alternative aux méthodes basées sur le filtre de Kalman. Dans cet article, nous dérivons les formules analytiques des racines moyenne-mobile d'un modèle à deux facteurs. Ensuite, nous proposons une application financière. Plus précisément, nous caractérisons la représentation GARCH(2,2) faible d'un modèle en temps continu et à volatilité stochastique quand la variance instantanée est la combinaison linéaire de deux processus auto-régressifs, comme pour les modèles affines, diffusion GARCH, CEV, Ornstein-Uhlenbeck et positifs, à fonctions propres, et SR-SARV.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2002s-92.

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Date of creation: 01 Dec 2002
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Handle: RePEc:cir:cirwor:2002s-92

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Keywords: Two-factor models; structural models; ARMA representation; Moving-average roots; continuous time stochastic volatility model; weak GARCH representation; modèles à deux facteurs; modèles structurels; représentation ARMA; racine moyenne-mobile; modèle en temps continu et à volatilité stochastique; représentation GARCH faible;

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