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An Ordinal Pattern Approach to Detect and to Model Leverage Effects and Dependence Structures Between Financial Time Series

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  • Alexander Schnurr

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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  • Alexander Schnurr, 2015. "An Ordinal Pattern Approach to Detect and to Model Leverage Effects and Dependence Structures Between Financial Time Series," Papers 1502.07321, arXiv.org.
    • Handle: RePEc:arx:papers:1502.07321
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    References listed on IDEAS

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    1. Carr, Peter & Wu, Liuren, 2007. "Stochastic skew in currency options," Journal of Financial Economics, Elsevier, vol. 86(1), pages 213-247, October.
    2. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    3. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    4. Almut Veraart & Luitgard Veraart, 2012. "Stochastic volatility and stochastic leverage," Annals of Finance, Springer, vol. 8(2), pages 205-233, May.
    5. H. Zarei & H. Jabbari, 2011. "Complete convergence of weighted sums under negative dependence," Statistical Papers, Springer, vol. 52(2), pages 413-418, May.
    6. Keller, K. & Sinn, M., 2005. "Ordinal analysis of time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(1), pages 114-120.
    7. Soo Sung, 2012. "Complete convergence for weighted sums of negatively dependent random variables," Statistical Papers, Springer, vol. 53(1), pages 73-82, February.
    8. Chstoph Bandt & Faten Shiha, 2007. "Order Patterns in Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(5), pages 646-665, September.
    9. Sinn, Mathieu & Keller, Karsten, 2011. "Estimation of ordinal pattern probabilities in Gaussian processes with stationary increments," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1781-1790, April.
    10. Dilip Madan & Marc Yor, 2011. "The S&P 500 Index as a Sato Process Travelling at the Speed of the VIX," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(3), pages 227-244.
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