Marcin Wątorek, Paweł Oświęcimka, Stanisław Drożdż
In this contribution we analyse statistical and multiscaling properties of WTI Crude oil prices expressed in US dollar in relation to the most traded currencies as well as to gold and to the SP500 futures prices. We show that in most of the cases the tails of the returns distribution of the considered financial instruments follow inverse cubic power law. The only exception is the Russian ruble for which the distribution tail scales with the exponent close to 2 which indicates dynamics closely related to the Lévy processes. From the perspective of multiscaling the analysed time series can be considered as multifractal structures with strongly left-sided asymmetry of the spectrum. However, the most interesting results we obtain in the case of multifractal cross-correlation analysis which is carried out by means of the multifractal cross-correlation analysis (MFCCA) and detrended cross-correlation coefﬁcient rq. Our results clearly show that all the considered instruments are multifractally cross-correlated with the oil prices and the strongest relationship with oil characterizes currencies of the countries extracting crude oil. Moreover, strength of the multifractal coupling depends on the considered time span. In the analysed time period the level of the cross-correlation increases systematically during the bear phase on the oil market and it saturates after the trend reversal in 1st half of 2016. MFCCA methodology is also applied to identify possible causal relations between considered observables. Analysis of the asymmetry in multifractal cross-correlation characteristics estimated for different variants of synchronization of the time series indicates dependence of the oil prices on the analysed currencies exchange rates. Likewise in the case of statistical analysis, exception is the Russian ruble rate which is influenced by oil prices. The causal connections are also analysed by means of the Granger causality test which confirms causal direction identified by multifractal methodology.