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This study examines the inner dynamics of multifractality between the carbon market (EU ETS) and four major fossil fuel energy markets Brent Crude Oil (BRN), Richards Bay Coal (RBC), UK Natural Gas (NGH2), and FTSE350 electricity index (FTSE35 from January 04, 2016, to March 04, 2022. First, we decompose the daily price changes by applying seasonal and trend decomposition using loess (STL). Then, we examine the inner dynamics of multifractality and cross-correlation by employing multifractal detrended fluctuation analysis (MFDFA) and m