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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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Author Info
D. Sornette (CNRS-Univ. Nice and Ucla)
W. -X. Zhou (UCLA and Ecust)
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/abs/cond-mat/0408166
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Paper provided by arXiv.org in its series Quantitative Finance 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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  1. Gary L. Shelley & Frederick H. Wallace, 2004. "Inflation, money, and real GDP in Mexico: a causality analysis," Applied Economics Letters, Taylor and Francis Journals, vol. 11(4), pages 223-225, March. [Downloadable!] (restricted)
  2. 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.
  3. Fountas, Stilianos & Karanasos, Menelaos & Kim, Jinki, 2002. "Inflation and output growth uncertainty and their relationship with inflation and output growth," Economics Letters, Elsevier, vol. 75(3), pages 293-301, May. [Downloadable!] (restricted)
  4. Fama, Eugene F, 1982. "Inflation, Output, and Money," Journal of Business, University of Chicago Press, vol. 55(2), pages 201-31, April. [Downloadable!] (restricted)
  5. Neil R. Ericsson & John S. Irons & Ralph W. Tryon, 2001. "Output and inflation in the long run," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 241-253. [Downloadable!]
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  6. D. Sornette & W-X. Zhou, 2002. "The US 2000-2002 market descent: how much longer and deeper?," Quantitative Finance, Taylor and Francis Journals, vol. 2(6), pages 468-481, June. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Ashley, R & Granger, C W J & Schmalensee, R, 1980. "Advertising and Aggregate Consumption: An Analysis of Causality," Econometrica, Econometric Society, vol. 48(5), pages 1149-67, July. [Downloadable!] (restricted)
  9. D. Sornette & W. -X. Zhou, 2002. "The US 2000-2002 Market Descent: How Much Longer and Deeper?," Quantitative Finance Papers cond-mat/0209065, arXiv.org. [Downloadable!]
  10. Hatemi-J, Abdulnasser & Irandoust, Manuchehr, 2002. "On the Causality between Exchange Rates and Stock Prices: A Note," Bulletin of Economic Research, Blackwell Publishing, vol. 54(2), pages 197-203, April.
  11. Robert Mundell, 1963. "Inflation and Real Interest," Journal of Political Economy, University of Chicago Press, vol. 71, pages 280. [Downloadable!] (restricted)
  12. D. Sornette & A. Johansen, 2001. "Significance of log-periodic precursors to financial crashes," Quantitative Finance Papers cond-mat/0106520, arXiv.org. [Downloadable!]
  13. Robert J. Barro, 1995. "Inflation and Economic Growth," NBER Working Papers 5326, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  14. 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. [Downloadable!] (restricted)
  15. Hyeon-Seung Huh & Hyun-Hoon Lee, 2002. "Asymmetric output cost of lowering inflation: empirical evidence for Canada," Canadian Journal of Economics, Canadian Economics Association, vol. 35(2), pages 218-238, May. [Downloadable!] (restricted)
  16. Chamberlain, Gary, 1982. "The General Equivalence of Granger and Sims Causality," Econometrica, Econometric Society, vol. 50(3), pages 569-81, May. [Downloadable!] (restricted)
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