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Abstract Multifractal detrended cross-correlation methodology is described and applied to Foreign exchange (Forex) market time series. Fluctuations of high-frequency exchange rates of eight major world currencies over 2010–2018 period are used to study cross-correlations. The study is motivated by fundamental questions in complex systems’ response to significant environmental changes and by potential applications in investment strategies, including detecting triangular arbitrage opportunities. Dominant multiscale cross-correlations between the exchange rates are found to typically occur at smaller fluctuation levels. However, hierarchical organization of ties expressed in terms of dendrograms, with a novel application of the multiscale cross-correlation coefficient, is more pronounced at large fluctuations. The cross-correlations are quantified to be stronger on average between those exchange rate pairs that are bound within triangular relations. Some pairs from outside triangular relations are, however, identified to be exceptionally strongly correlated as compared to the average strength of triangular correlations. This in particular applies to those exchange rates that involve Australian and New Zealand dollars and reflects their economic relations. Significant events with impact on the Forex are shown to induce triangular arbitrage opportunities which at the same time reduce cross-correlations on the smallest timescales and act destructively on the multiscale organization of correlations. In 2010–2018, such instances took place in connection with the Swiss National Bank intervention and the weakening of British pound sterling accompanying the initiation of Brexit procedure. The methodology could be applicable to temporal and multiscale pattern detection in any time series.
Gębarowski et al. (Fri,) studied this question.