# 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.
Keywords :
Type de document :
Pré-publication, Document de travail
2012
Domaine :

https://hal.archives-ouvertes.fr/hal-00716469
Contributeur : Jean-Marc Bardet <>
Soumis le : samedi 15 décembre 2012 - 18:42:54
Dernière modification le : mardi 26 février 2013 - 20:01:39
Document(s) archivé(s) le : dimanche 18 décembre 2016 - 02:14:32

### Fichiers

Fichiers produits par l'(les) auteur(s)

### Identifiants

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

### Citation

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

Consultations de
la notice

## 247

Téléchargements du document