Abstract
We introduce two types of ordinal pattern dependence between time series. Positive (resp. negative) ordinal pattern dependence can be seen as a non-paramatric and in particular non-linear counterpart to positive (resp. negative) correlation. We show in an explorative study that both types of this dependence show up in real world financial data.
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Notes
We state below how to deal with the case \(x_n=x_{n+1}\).
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Acknowledgments
The author wishes to thank two anonymous referees for their work. Their comments have helped to improve the paper. Furthermore he wishes to thank B. Funke (TU Dortmund) for carefully reading the manuscript and A. Dürre (TU Dortmund) for the implementation in R. The financial support of the DFG (German science Foundation) SFB 823: Statistical modeling of nonlinear dynamic processes (project C5) is gratefully acknowledged.
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Schnurr, A. An ordinal pattern approach to detect and to model leverage effects and dependence structures between financial time series. Stat Papers 55, 919–931 (2014). https://doi.org/10.1007/s00362-013-0536-8
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DOI: https://doi.org/10.1007/s00362-013-0536-8