Exploring the multifractality in the precious metal market

Abstract

This study proposes a novel approach to investigating the multifractality of time series using the multifractal cross-correlation detrended moving average analysis (MF-X-DMA). The study demonstrates the behavioral differences of MF-X-DMA in coherent and non-coherent time periods. Due to the lack of a mechanism to capture the dynamical cross-correlation in time series, correlated time series with multifractal structure present a barrier for analysis. The study shows that when the wavelet coherence method is applied to time series, co-movement between time series can be easily captured in certain time intervals, providing an efficient way to find time intervals to apply MF-X-DMA. The study applies the wavelet coherence method to the daily spot prices of gold and platinum from January 1987. It shows that the wavelet coherence method is an excellent engine to extract designated time series in certain frequency and time intervals, eliminating the need for windowing or shuffling methods. Additionally, the study observes a long-term power law cross-correlation using detrended cross-correlation analysis coefficients of inversed series for both low-correlated and high-correlated series. Finally, the findings indicate that MF-X-DMA leads to superior results compared to MF-DFA when provided with highly correlated data.