Infinite-Dimensional Autoregressive Systems and the Generalized Dynamic Factor Model

Lippi, Marco

Journal de la société française de statistique, Tome 153 (2012) no. 1, pp. 71-81.

Le Modèle à Facteurs Dynamiques Généralisé est habituellement représenté comme une moyenne mobile infinie des chocs communs à laquelle s’ajoutent des composantes idiosyncratiques. Dans cet article, nous expliquons que cette représentation n’est que la solution (sous forme réduite) d’un système d’équations plus profond, structural, de dimension infinie, et contenant à la fois une partie autorégressive et une partie à moyenne mobile. Nous livrons des conditions qui garantissent que les solutions de tels systèmes sont faiblement stationnaires et nous analysons leur décomposition en composantes communes et idiosyncratiques. Enfin, nous établissons des liens avec la mémoire longue qui est engendrée par agrégation.

The Generalized Dynamic Factor Model is usually represented as an infinite-dimensional moving average of the common shocks plus idiosyncratic components. Here I argue that such representation can only be the solution (reduced form) of a deeper, structural, infinite-dimensional system of equations which contain both an autoregressive and a moving average part. I give conditions for the solutions of such infinite-dimensional systems to make sense and be weakly stationary, and study their decomposition into common and idiosyncratic components. Interesting links to long memory as generated by aggregation are also shown.

Keywords: Infinite-Dimensional Datasets, Generalized Dynamic Factor Models
Mot clés : Ensembles de données de dimension infinie, Modèle à Facteurs Dynamiques Généralisé

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