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A test of the null of integer integration against the alternative of fractional integration

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  • Cho, Cheol-Keun
  • Amsler, Christine
  • Schmidt, Peter

Abstract

This paper proposes a test of the null of integer integration against the alternative of fractional integration. The null of integer integration is satisfied if the series is either I(0) or I(1). We reject the null if the KPSS test rejects I(0) and a unit root test rejects I(1). We suggest a new unit root test (a lower-tail KPSS test applied to the differenced data) to use in this procedure. We provide critical values under standard asymptotics and fixed-b asymptotics. We prove the consistency of this testing procedure against I(d) alternatives with 0

Suggested Citation

  • Cho, Cheol-Keun & Amsler, Christine & Schmidt, Peter, 2015. "A test of the null of integer integration against the alternative of fractional integration," Journal of Econometrics, Elsevier, vol. 187(1), pages 217-237.
    • Handle: RePEc:eee:econom:v:187:y:2015:i:1:p:217-237
    DOI: 10.1016/j.jeconom.2015.02.023
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    2. Richard T. Baillie & Dooyeon Cho & Seunghwa Rho, 2023. "Approximating long-memory processes with low-order autoregressions: Implications for modeling realized volatility," Empirical Economics, Springer, vol. 64(6), pages 2911-2937, June.
    3. Seong Yeon Chang & Pierre Perron, 2017. "Fractional Unit Root Tests Allowing for a Structural Change in Trend under Both the Null and Alternative Hypotheses," Econometrics, MDPI, vol. 5(1), pages 1-26, January.

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    More about this item

    Keywords

    Fractionally integrated process; Short memory; Unit root;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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