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An adaptive estimator of the memory parameter and the goodness-of-fit test using a multidimensional increment ratio statistic

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  • Bardet, Jean-Marc
  • Dola, Béchir

Abstract

The increment ratio (IR) statistic was first defined and studied in Surgailis et al. (2007) [19] for estimating the memory parameter either of a stationary or an increment stationary Gaussian process. Here three extensions are proposed in the case of stationary processes. First, a multidimensional central limit theorem is established for a vector composed by several IR statistics. Second, a goodness-of-fit χ2-type test can be deduced from this theorem. Finally, this theorem allows to construct adaptive versions of the estimator and the test which are studied in a general semiparametric frame. The adaptive estimator of the long-memory parameter is proved to follow an oracle property. Simulations attest to the interesting accuracies and robustness of the estimator and the test, even in the non Gaussian case.

Suggested Citation

  • Bardet, Jean-Marc & Dola, Béchir, 2012. "An adaptive estimator of the memory parameter and the goodness-of-fit test using a multidimensional increment ratio statistic," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 222-240.
    • Handle: RePEc:eee:jmvana:v:105:y:2012:i:1:p:222-240
    DOI: 10.1016/j.jmva.2011.09.003
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    References listed on IDEAS

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    1. E. Moulines & F. Roueff & M. S. Taqqu, 2007. "On the Spectral Density of the Wavelet Coefficients of Long‐Memory Time Series with Application to the Log‐Regression Estimation of the Memory Parameter," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(2), pages 155-187, March.
    2. Liudas Giraitis & Peter M. Robinson & Alexander Samarov, 1997. "Rate Optimal Semiparametric Estimation Of The Memory Parameter Of The Gaussian Time Series With Long‐Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(1), pages 49-60, January.
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    1. 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.

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