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On Distinguishing Between Random Walk And Change In The Mean Alternatives

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  • Aue, Alexander
  • Horváth, Lajos
  • Hušková, Marie
  • Ling, Shiqing

Abstract

We study test procedures that detect structural breaks in underlying data sequences. In particular, we wish to discriminate between different reasons for these changes, such as (1) shifting means, (2) random walk behavior, and (3) constant means but innovations switching from stationary to difference stationary behavior. Almost all procedures presently available in the literature are simultaneously sensitive to all three types of alternatives.The test statistics under investigation are based on functionals of the partial sums of observations. These cumulative sum–type (CUSUM-type) statistics have limit distributions if the mean remains constant and the errors satisfy the central limit theorem but tend to infinity in the case when any of the alternatives (1), (2), or (3) holds. On removing the effect of the shifting mean, however, divergence of the test statistics will only occur under the random walk behavior, which in turn enables statisticians not only to detect structural breaks but also to specify their causes.The results are underlined by a simulation study and an application to returns of the German stock index DAX.

Suggested Citation

  • Aue, Alexander & Horváth, Lajos & Hušková, Marie & Ling, Shiqing, 2009. "On Distinguishing Between Random Walk And Change In The Mean Alternatives," Econometric Theory, Cambridge University Press, vol. 25(2), pages 411-441, April.
    • Handle: RePEc:cup:etheor:v:25:y:2009:i:02:p:411-441_09
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    Cited by:

    1. Holger Dette & Dominik Wied, 2016. "Detecting relevant changes in time series models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 371-394, March.
    2. Wingert, Simon & Mboya, Mwasi Paza & Sibbertsen, Philipp, 2020. "Distinguishing between breaks in the mean and breaks in persistence under long memory," Economics Letters, Elsevier, vol. 193(C).
    3. Marco R. Barassi & Nicola Spagnolo & Yuqian Zhao, 2018. "Fractional Integration Versus Structural Change: Testing the Convergence of $$\hbox {CO}_{2}$$ CO 2 Emissions," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 71(4), pages 923-968, December.

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