Department of Economics and Business Economics

Discriminating between fractional integration and spurious long memory

Research output: Working paperResearch


  • rp14_19

    Submitted manuscript, 1.02 MB, PDF document

  • Niels Haldrup
  • Robinson Kruse, Leibniz University of Hannover, Germany
Fractionally integrated processes have become a standard class of models to describe the long memory features of economic and financial time series data. However, it has been demonstrated in numerous studies that structural break processes and non-linear features can often be confused as being long memory. The question naturally arises whether it is possible empirically to determine the source of long memory as being genuinely long memory in the form of a fractionally integrated process or whether the long range dependence is of a different nature. In this paper we suggest a testing procedure that helps discriminating between such processes. The idea is based on the feature that nonlinear transformations of stationary fractionally integrated Gaussian processes decrease the order of memory in a specific way which is determined by the Hermite rank of the transformation. In principle, a non-linear transformation of the series can make the series short memory I(0). We suggest using the Wald test of Shimotsu (2007) to test the null hypothesis that a vector time series of properly transformed variables is I(0). Our testing procedure is designed such that even non-stationary fractionally integrated processes are permitted under the null hypothesis. The test is shown to have good size and to be robust against certain types of deviations from Gaussianity. The test is also shown to be consistent against a broad class of processes that are non-fractional but still exhibit (spurious) long memory. In particular, the test is shown to have excellent power against a class of stationary and non-stationary random level shift models as well as Markov switching GARCH processes where the break and transition probabilities are allowed to be time varying.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages42
Publication statusPublished - 30 Jun 2014
SeriesCREATES Research Papers

    Research areas

  • Long memroy, Fractional integration, Non-linear models, Structural breaks, Random level shifts, Hermite polynomials, Realized volatility, Inflation

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