Long memory in international financial markets trends and short movements during 2008 financial crisis based on variational mode decomposition and detrended fluctuation analysis

• International Stock markets are analyzed by variational mode de composition.
• Trend and shorts variations in price and return series are characterized.
• Detrended fluctuation analysis and R/S analysis are used to estimate Hurst exponent of each mode.
• For all markets and before, during, and after 2008 financial crisis, it is found that price and return trends are persistent, whilst their short variations are anti-persistent.

The purpose of this study is to investigate long-range dependence in trend and short variation of stock market price and return series before, during, and after 2008 financial crisis. Variational mode decomposition (VMD), a newly introduced technique for signal processing, is adopted to decompose stock market data into a finite set of modes so as to obtain long term trends and short term movements of stock market data. Then, the detrended fluctuation analysis (DFA) and range scale (R/S) analysis are used to estimate Hurst exponent in each variational mode obtained from VMD. For both price and return series, the empirical results from twelve international stock markets show evidence that long term trends are persistent, whilst short term variations are anti-persistent before, during, and after 2008 financial crisis.