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Nonsense regressions due to neglected time-varying means

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Abstract

Regressions of two independent time series are considered. The variables are covariance stationary but display time-varying although not trending means. Two prominent examples are level shifts due to structural breaks and seasonally varying means. If the variation of the means is not taken into account, this induces nonsense correlation. The asymptotic treatment is supplemented by experimental evidence.

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Authors and Affiliations

  1. Institute of Statistics and Econometrics, Free University of Berlin, Boltzmannstraße 20, 14195, Berlin, Germany

    Uwe Hassler

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  1. Uwe Hassler
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Correspondence to Uwe Hassler.

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This work was carried out while visiting Universidad Carlos III de Madrid. Financial support from the European Commission through the Training and Mobility of Researchers programme is gratefully acknowledged. An earlier version was circulated as Universidad Carlos III working paper 99-78. I am grateful to Artur da Silva Lopes for comments that improved the presentation.

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Hassler, U. Nonsense regressions due to neglected time-varying means. Statistical Papers 44, 169–182 (2003). https://doi.org/10.1007/s00362-003-0144-0

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  • DOI: https://doi.org/10.1007/s00362-003-0144-0

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