On the ARCH model with stationary liquidity

Voutilainen, Marko; Ilmonen, Pauliina; Torres, Soledad; Tudor, Ciprian; Viitasaari, Lauri

Type de document :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1007/s00184-020-00779-x

Titre :

On the ARCH model with stationary liquidity

Auteur(s) :

Voutilainen, Marko [Auteur]
Ilmonen, Pauliina [Auteur]
Torres, Soledad [Auteur]
Tudor, Ciprian [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Viitasaari, Lauri [Auteur]

Titre de la revue :

Metrika

Pagination :

195-224

Éditeur :

Springer Verlag

Date de publication :

2020-06-24

ISSN :

0026-1335

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

Abstract The classical ARCH model together with its extensions have been widely applied in the modeling of financial time series. We study a variant of the ARCH model that takes account of liquidity given by a positive ...
Lire la suite >Abstract The classical ARCH model together with its extensions have been widely applied in the modeling of financial time series. We study a variant of the ARCH model that takes account of liquidity given by a positive stationary process. We provide minimal assumptions that ensure the existence and uniqueness of the stationary solution for this model. Moreover, we give necessary and sufficient conditions for the existence of the autocovariance function. After that, we derive an AR(1) characterization for the stationary solution yielding Yule–Walker type quadratic equations for the model parameters. In order to define a proper estimation method for the model, we first show that the autocovariance estimators of the stationary solution are consistent under relatively mild assumptions. Consequently, we prove that the natural estimators arising out of the quadratic equations inherit consistency from the autocovariance estimators. Finally, we illustrate our results with several examples and a simulation study.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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On the ARCH model with stationary liquidity

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