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Semiparametric Stationarity and Fractional Unit Roots Tests Based on Data-Driven Multidimensional Increment Ratio Statistics

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  • Bardet Jean-Marc
  • Dola Béchir

    (SAMM, Université Panthéon-Sorbonne (Paris I), 90 rue de Tolbiac, 75013 Paris, France)

Abstract

In this paper, we show that the central limit theorem (CLT) satisfied by the data-driven Multidimensional Increment Ratio (MIR) estimator of the memory parameter d established in Bardet and Dola (2012. Adaptive Estimator of the Memory Parameter and Goodness-of-Fit Test Using a Multidimensional Increment Ratio Statistic.” Journal of Multivariate Analysis 105:222–40) for dϵ(–0.5, 0.5) can be extended to a semiparametric class of Gaussian fractionally integrated processes with memory parameter dϵ(–0.5, 1.25). Since the asymptotic variance of this CLT can be estimated, by data-driven MIR tests for the two cases of stationarity and non-stationarity, so two tests are constructed distinguishing the hypothesis d

Suggested Citation

  • Bardet Jean-Marc & Dola Béchir, 2016. "Semiparametric Stationarity and Fractional Unit Roots Tests Based on Data-Driven Multidimensional Increment Ratio Statistics," Journal of Time Series Econometrics, De Gruyter, vol. 8(2), pages 115-153, July.
    • Handle: RePEc:bpj:jtsmet:v:8:y:2016:i:2:p:115-153:n:3
    DOI: 10.1515/jtse-2014-0031
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    References listed on IDEAS

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