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ARFIMA Process : Tests and Applications at a White Noise Process, A Random Walk Process and the Stock Exchange Index CAC 40

Bourbonnais, Régis; Maftei, Magda Mara (2012), ARFIMA Process : Tests and Applications at a White Noise Process, A Random Walk Process and the Stock Exchange Index CAC 40, Economic Computation and Economic Cybernetics Studies and Research, 46, 1, p. 5-17

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Type
Article accepté pour publication ou publié
Date
2012-01
Journal name
Economic Computation and Economic Cybernetics Studies and Research
Volume
46
Number
1
Publisher
ASE Bucharest
Pages
5-17
Metadata
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Author(s)
Bourbonnais, Régis

Maftei, Magda Mara
Académie des Etudes Economiques de Bucarest
Abstract (FR)
L’hypothèse de linéarité est admise implicitement pour le processus générateur d’une chronique qui obéit à un ARIMA. C’est pourquoi nous abordons dans ce papier la recherche de mémoire longue dans les processus : les modèles ARIMA fractionnaire, notés ARFIMA, pour lesquels d ou D, les degrés de différenciation des filtres ne sont pas des entiers. Après avoir présenté les caractéristiques des processus ARFIMA, nous abordons les tests de mémoire longue (statistiques Rescaled Range, Lo et R/S*de Moody et Wu). Enfin trois exemples et tests sur un processus de bruit blanc, un processus DS et l’indice boursier de la bourse de Paris (CAC40) illustreront la méthode.
Abstract (EN)
The assumption of linearity is implicitly accepted in the process which generates a time series condition submitted to a ARIMA. That is why, in this paper, we shall discuss the research of long memory in the processes: the fractional ARIMA models, denoted as ARFIMA, where d and D, the degree of differentiation of the filters is not integer. After presenting the characteristics of the ARFIMA process, we shall discuss the long-memory tests (statistics rescaled Range Lo and R/S* Moody and Wu). Finally three examples and tests on a white noise process, a random walk model and the stock index of Paris Stock Exchange (CAC40) will illustrate the method.
Subjects / Keywords
Long-memory test; non stationary processes; ARIMA process; ARFIAM process
JEL
C12 - Hypothesis Testing: General
C30 - General
C32 - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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