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Non-parametric Determination of Real-Time Lag Structure between Two Time Series: the "Optimal Thermal Causal Path" Method

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  • D. Sornette

    (CNRS-Univ. Nice and Ucla)

  • W. -X. Zhou

    (UCLA and Ecust)

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    Abstract

    We introduce a novel non-parametric methodology to test for the dynamical time evolution of the lag-lead structure between two arbitrary time series. The method consists in constructing a distance matrix based on the matching of all sample data pairs between the two time series. Then, the lag-lead structure is searched as the optimal path in the distance matrix landscape that minimizes the total mismatch between the two time series, and that obeys a one-to-one causal matching condition. To make the solution robust to the presence of large noise that may lead to spurious structures in the distance matrix landscape, we then generalize this optimal search by introducing a fuzzy search by sampling over all possible paths, each path being weighted according to a multinomial logit or equivalently Boltzmann factor proportional to the exponential of the global mismatch of this path. We present the efficient transfer matrix method that solves the problem and test it on simple synthetic examples to demonstrate its properties and usefulness compared with the standard running-time cross-correlation method. We then apply our `Optimal Thermal Causal Path'' method to the question of the causality between ......

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    File URL: http://arxiv.org/pdf/cond-mat/0408166
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    Paper provided by arXiv.org in its series Papers with number cond-mat/0408166.

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    Date of creation: Aug 2004
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    Publication status: Published in Quantitative Finance 5, 577-591 (2005). See also Journal of Macroeconomics 28, 195-224 (2006) for more details on the methodology.
    Handle: RePEc:arx:papers:cond-mat/0408166

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    Web page: http://arxiv.org/

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    1. Hatemi-J, Abdulnasser & Irandoust, Manuchehr, 2002. "On the Causality between Exchange Rates and Stock Prices: A Note," Bulletin of Economic Research, Wiley Blackwell, vol. 54(2), pages 197-203, April.
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    4. Fischer, Stanley, 1974. "Money and the Production Function," Economic Inquiry, Western Economic Association International, vol. 12(4), pages 517-33, December.
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    9. Didier Sornette & Wei-Xing Zhou, 2002. "The US 2000-2002 market descent: How much longer and deeper?," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 468-481.
    10. Strozzi, Fernanda & Zaldı́var, José-Manuel & Zbilut, Joseph P, 2002. "Application of nonlinear time series analysis techniques to high-frequency currency exchange data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(3), pages 520-538.
    11. Kevin J. Lansing, 2000. "Exploring the causes of the Great Inflation," FRBSF Economic Letter, Federal Reserve Bank of San Francisco, issue jul7.
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    13. Geweke, John, 1984. "Inference and causality in economic time series models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 19, pages 1101-1144 Elsevier.
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    16. Gary Shelley & Frederick Wallace, 2004. "Inflation, money, and real GDP in Mexico: a causality analysis," Applied Economics Letters, Taylor & Francis Journals, vol. 11(4), pages 223-225.
    17. Apergis, Nicholas, 2004. "Inflation, output growth, volatility and causality: evidence from panel data and the G7 countries," Economics Letters, Elsevier, vol. 83(2), pages 185-191, May.
    18. D. Sornette & W. -X. Zhou, 2002. "The US 2000-2002 Market Descent: How Much Longer and Deeper?," Papers cond-mat/0209065, arXiv.org.
    19. Robert Mundell, 1963. "Inflation and Real Interest," Journal of Political Economy, University of Chicago Press, vol. 71, pages 280.
    20. Hyeon-seung Huh, 2002. "Estimating Asymmetric Output Cost of Lowering Inflation for Australia," Southern Economic Journal, Southern Economic Association, vol. 68(3), pages 600-616, January.
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