Semiparametric stationarity tests based on adaptive multidimensional increment ratio statistics

Abstract : 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.
Type de document :
Pré-publication, Document de travail
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Contributeur : Jean-Marc Bardet <>
Soumis le : samedi 15 décembre 2012 - 18:42:54
Dernière modification le : mardi 28 novembre 2017 - 01:18:19
Document(s) archivé(s) le : dimanche 18 décembre 2016 - 02:14:32


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  • HAL Id : hal-00716469, version 2
  • ARXIV : 1207.2453



Jean-Marc Bardet, Béchir Dola. Semiparametric stationarity tests based on adaptive multidimensional increment ratio statistics. 2012. 〈hal-00716469v2〉



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