Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-08-07
Quantitative Finance 5, 577-591 (2005). See also Journal of Macroeconomics 28, 195-224 (2006) for more details on the methodol
Physics
Condensed Matter
Statistical Mechanics
37 Elsevier pages including 13 eps figures
Scientific paper
10.1080/14697680500383763
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 ......
Sornette Didier
Zhou Wei-Xing
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