•Machine learning methods used to forecast end-of-month exchange rates 1-month forward.•Fundamentals from PPP, UIRP and Taylor-rule models allow to beat the random walk.•Study for 1973–2014 period, 12 major industrial country currencies vs U.S. dollar.•RMSE, directional and economic criteria of evaluation; multiple robustness checks. Using methods from machine learning we show that fundamentals from simple exchange rate models (PPP or UIRP) or Taylor-rule based models lead to improved exchange rate forecasts for major currencies over the floating period era 1973–2014 at a 1-month forecast horizon which beat the no-change forecast. Fundamentals thus contain useful information and exchange rates are forecastable even for short horizons. Such conclusions cannot be obtained when using rolling or recursive OLS regressions as used in the literature. The methods we use – sequential ridge regression and the exponentially weighted average strategy, both with discount factors – do not estimate an underlying model but combine the fundamentals to directly output forecasts.