Outlining guidelines for the application of the MF-DCCA in financial time series: non-stationary vs stationary

This paper disrupts mistaken applications of multifractal approaches in financial time series. Specifically, we have examined the non-linear cross-correlation between the São Paulo time series of the weekly price of ethanol and the other 14 Brazilian capitals' time series of the weekly price of the same biofuel using the Multifractal Detrended Cross-Correlation Analysis (MF-DCCA). Given the statistical peculiars of stationary and non-stationary financial time series, we suggest two possibilities for employing multifractal approaches to these time series. Our findings shed light and promote alignment between basic time series analysis techniques and multifractal dynamics. Also, we discover that the use of MF-DCCA is highly impacted by choice of time series (stationary or non-stationary).