Statistical Papers

, Volume 54, Issue 4, pp 977–991 | Cite as

Fractional integration versus level shifts: the case of realized asset correlations

  • Philip Bertram
  • Robinson Kruse
  • Philipp SibbertsenEmail author
Regular Article


Long memory has been widely documented for realized financial market volatility. As a novelty, we consider daily realized asset correlations and we investigate whether the observed persistence is (i) due to true long memory (i.e. fractional integration) or (ii) artificially generated by some structural break processes. These two phenomena are difficult to be distinguished in practice. Our empirical results strongly indicate that the hyperbolic decay of the autocorrelation functions of pair-wise realized correlation series is indeed not driven by a truly fractionally integrated process. This finding is robust against user specific parameter choices in the applied test statistic and holds for all 15 considered time series. As a next step, we apply simple models with deterministic level shifts. When selecting the number of breaks, estimating the breakpoints and the corresponding structural break models we find a substantial degree of co-movement between the realized correlation series hinting at co-breaking. The estimated structural break models are interpreted in the light of the historic economic and financial development.


Long memory Fractional integration Structural breaks  Realized correlation 

JEL Classification

C12 C22 



The authors thank two anonymous referees for carefully reading the paper. Robinson Kruse gratefully acknowledges financial support from CREATES funded by the Danish National Research Foundation. The financial support by the Deutsche Forschungsgemeinschaft (DFG) is gratefully acknowledged.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Philip Bertram
    • 1
  • Robinson Kruse
    • 1
    • 2
  • Philipp Sibbertsen
    • 1
    Email author
  1. 1.School of Economics and Management, Institute for StatisticsLeibniz University HannoverHannoverGermany
  2. 2.CREATES, School of Economics and ManagementAarhus UniversityAarhus CDenmark

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