2012/07/10 by Jean‐Marc Bardet, Jean-Marc Bardet, Bardet, Jean-Marc +2 · 1 citation
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Market Dynamics and Volatility #Monetary Policy and Economic Impact #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1207.2453
openalex publication_date 2012/07/10 · arxiv created 2012/12/15 · arxiv updated 2012/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ∈ (-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 ≥ 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.