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

Régis Bourbonnais and Magda Mara Maftei
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Régis Bourbonnais: LEDa - Laboratoire d'Economie de Dauphine - IRD - Institut de Recherche pour le Développement - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique
Magda Mara Maftei: A.S.E. - The Bucharest University of Economic Studies / Academia de Studii Economice din Bucureşti

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Abstract: 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.

Keywords: Long-memory test; non stationary processes; ARIMA process; ARFIAM process (search for similar items in EconPapers)
Date: 2012-01
Note: View the original document on HAL open archive server: https://hal.science/hal-01491880v1
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Citations: View citations in EconPapers (3)

Published in Journal of Economic Computation and Economic Cybernetics Studies and Research, 2012, 46 (1)

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