Connection between macroeconomic variables and foreign exchange (FX) rates evaluated in the context of out-of-sample forecasting is a well-known problem in economics. We propose a method that utilizes stochastic models based on jump processes (namely the normal inverse Gaussian and Meixner models), combines them with macroeconomic fundamentals, and using a moving (rolling or recursive) regularized estimation procedure produces forecasts of FX rates. These are compared to benchmark models, namely the direct forecast and the Gauss model forecast. Empirical out-of-sample experiments are performed on EUR/USD and USD/DKK currencies.Keywords: exchange rates forecasting, jump processes, macroeconomic fundamentals, out-ofsample testing, cross-validation JEL Classification: C46, C53, F37
. IntroductionSurveying the published work, we may find a lot of evidence against usefulness of macroeconomic information for the prediction of foreign exchange (FX) rates. This problem is sometimes labelled as the exchange rate disconnect puzzle and originates from Meese and Rogoff (1983). In the literature, mostly they conclude that even though the standard macroeconomic models are able to (at least partially) describe in-sample movement of FX rate, however, out-of-sample forecast is rarely better than a (no-change) forecast of a random walk (with or without drift). There is a vast amount of literature on this topiccovering different methods of prediction, using various economic fundamentals, all applied on miscellaneous FX rates and time periods; for a good overview (and an exhaustive list of references) see the comprehensive study Rossi (2013) for instance. We try to provide a novel approach to forecasting of FX rates combining stochastic models with jumps, predictors based on standard macroeconomic models such as purchasing power parity, monetary fundamentals model, and Taylor-rule model, and techniques of regularized estimation with cross-validation. Although there is a literature about modelling of FX rates with jump models employed -Jiang (1998), Božović (2008), Busch et al. (2005), Nirei and Sushko (2011), Bates (1996), Nekhili et al. (2002), Maheu and McCurdy (2008) among others -to our knowledge, combining jump processes with macroeconomic information in order to predict FX rates seems to be new. Also note that we work with the infinite activity jump processes (namely the normal inverse Gaussian (NIG) and Meixner models), which is not a very commonplace practice in the literature concerning FX rates forecasting.