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Searching for fractional evidence using combined unit root tests

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  • Mármol, Francesc

Abstract

It has become a fully accepted rule in applied work that rejection of both the difference stationarity and trend stationarity null hypotheses, could imply the possibility that the underlying time series behaves as a fractionally integrated process. In this paper we prove this claim in a rigorous way by showing the consistency of the customary Dickey-Fuller and KPSS tests against fractional alternatives. It is shown that the combined use of both tests only achieves consistency if two-tailed tests are implemented.

Suggested Citation

  • Mármol, Francesc, 1998. "Searching for fractional evidence using combined unit root tests," DES - Working Papers. Statistics and Econometrics. WS 10613, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:10613
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    References listed on IDEAS

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    Cited by:

    1. Kramer, Walter & Marmol, Francesc, 2004. "The power of residual-based tests for cointegration when residuals are fractionally integrated," Economics Letters, Elsevier, vol. 82(1), pages 63-69, January.
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    3. Andersen, Torben G. & Varneskov, Rasmus T., 2021. "Consistent inference for predictive regressions in persistent economic systems," Journal of Econometrics, Elsevier, vol. 224(1), pages 215-244.
    4. Sibbertsen, Philipp & Kramer, Walter, 2006. "The power of the KPSS-test for cointegration when residuals are fractionally integrated," Economics Letters, Elsevier, vol. 91(3), pages 321-324, June.

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