Outperforming the naïve Random Walk forecast of foreign exchange daily closing prices using Variance Gamma and normal inverse Gaussian Levy processes

This work demonstrates that forecast of foreign exchange (FX) daily closing prices using the normal inverse Gaussian (NIG) and Variance Gamma (VG) Levy processes outperform the naïve Random Walk model. We use the open software R to estimate NIG and VG distribution parameters and perform several classical goodness–of -fits test to select best models. Seven currency pairs can be forecasted by both Levy processes: TND/GBP, EGP/EUR, EUR/GBP, EUR/JPY, JOD/JPY, USD/GBP, and XAU/USD, while USD/JPY and QAR/JPY can be forecasted with the VG process only. RMSE values show that NIG and VG forecast are comparable, and both outperform the naïve Random Walk out of sample. Appended R-codes are original.