Abstract
We extend the concept of statistical symmetry as the invariance of a probability distribution under transformation to analyze binary sign time series data of price difference from the foreign exchange market. We model segments of the sign time series as Markov sequences and apply a local hypothesis test to evaluate the symmetries of independence and time reversion in different periods of the market. For the test, we derive the probability of a binary Markov process to generate a given set of number of symbol pairs. Using such analysis, we could not only segment the time series according the different behaviors but also characterize the segments in terms of statistical symmetries. As a particular result, we find that the foreign exchange market is essentially time reversible but this symmetry is broken when there is a strong external influence.
MeSH terms
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Financial Management / statistics & numerical data*
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Markov Chains
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Statistics as Topic*
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Time Factors
Grants and funding
Author A.M.Y.R.S. acknowledges funding from Monbukagakusho MEXT Scholarship (Japanese Ministry of Education, Culture, Sports, Science and Technology). This work was partially supported by a Grant-in-Aid for Scientific Research (B) 26310207. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Author H.T. is employed by Sony Computer Science Laboratories. Sony Computer Science Laboratories provided support in the form of salaries for author H.T., but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of manuscript. All authors were involved in all stages of the present work.