Open AccessDetection of statistical asymmetries in non-stationary sign time series: Analysis of foreign exchange data
Author(s) -
Arthur Matsuo Yamashita Rios de Sousa,
Hideki Takayasu,
Misako Takayasu
Publication year - 2017
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0177652
Subject(s) - sign (mathematics) , series (stratigraphy) , markov process , time series , independence (probability theory) , mathematics , statistical hypothesis testing , markov chain , foreign exchange market , statistical physics , symmetry (geometry) , binary number , econometrics , statistics , foreign exchange , physics , mathematical analysis , economics , geometry , paleontology , monetary economics , biology , arithmetic
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.