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

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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.

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  1. 1.

    For definitions and details regarding construction of realized (co-)variances we refer the interested reader to Chiriac and Voev (2011).

  2. 2.

    Here and in the following tables we give only the results for General Electrics as the reference series to safe space. The results are similar for all other series as reference series but for General Electrics we find the highest heterogeneity showing best the properties of the data.


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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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Correspondence to Philipp Sibbertsen.

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This article is dedicated to Walter Krämer, a most inspiring econometrician, teacher and friend.

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Bertram, P., Kruse, R. & Sibbertsen, P. Fractional integration versus level shifts: the case of realized asset correlations. Stat Papers 54, 977–991 (2013). https://doi.org/10.1007/s00362-013-0513-2

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  • Long memory
  • Fractional integration
  • Structural breaks
  • Realized correlation

JEL Classification

  • C12
  • C22