HAL : hal-00716469, version 2

arXiv : 1207.2453

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v2 (15-12-2012)

Semiparametric stationarity tests based on adaptive multidimensional increment ratio statistics

Jean-Marc Bardet 1, Béchir Dola 1

(2012)

In this paper, we show that the adaptive multidimensional increment ratio estimator of the long range memory parameter defined in Bardet and Dola (2012) satisfies a central limit theorem (CLT in the sequel) for a large semiparametric class of Gaussian fractionally integrated processes with memory parameter $d \in (-0.5,1.25)$. Since the asymptotic variance of this CLT can be computed, tests of stationarity or nonstationarity distinguishing the assumptions $d<0.5$ and $d \geq 0.5$ are constructed. These tests are also consistent tests of unit root. Simulations done on a large benchmark of short memory, long memory and non stationary processes show the accuracy of the tests with respect to other usual stationarity or nonstationarity tests (LMC, V/S, ADF and PP tests). Finally, the estimator and tests are applied to log-returns of famous economic data and to their absolute value power laws.

1 :	Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM)
	Université Paris I - Panthéon-Sorbonne

Domaine

:

Mathématiques/Statistiques Statistiques/Théorie

Mots Clés : Gaussian fractionally integrated processes – Adaptive semiparametric estimators of the memeory parameter – test of long-memory – stationarity test – unit root test.

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Contributeur : Jean-Marc Bardet <>

Soumis le : Samedi 15 Décembre 2012, 18:42:54

Dernière modification le : Mardi 26 Février 2013, 20:01:39