Semiparametric stationarity tests based on adaptive multidimensional increment ratio statistics

Jean-Marc Bardet (1) , Béchir Dola (1)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)

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.

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

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

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