Une généralisation des processus ARMA

Esmeralda Gonçalves

Annals of Economics and Statistics, 1987, issue 5, 109-145

Abstract: The aim of this paper is the introduction of a class of models generalizing the usual ARMA models and giving possible solutions for two difficulties encountered in ARMA modelling, the identification step, i.e. the estimation of the autoregressive and moving average orders, and the phenomenas of under and over differencing. The studied processes, called MADE processes (Moving Average satisfying a Difference Equation) are regular stationnary processes, whose infinite moving average expansion: has coefficients satisfying a difference equation with coefficients which are polynomials of degree 1. We discuss the existence and the uniqueness of such processes, we verify that this class contains as particular cases the ARMA processes and the long memory models studied by Granger. Then we give a number of results concerning the autocovariance function, the spectral density function...

Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:adr:anecst:y:1987:i:5:p:109-145

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