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

Semiparametric stationarity tests based on adaptive multidimensional increment ratio statistics