Macroeconomic and aggregate financial series were shown empirically to share an unconventional form of cyclical and persistent dynamics, whose functional form was obtained from the solution of general-equilibrium models with heterogeneous firms. The econometric modeling of equations that link such series requires a new methodology, as existing parametric techniques can cause paradoxical regression results and omit predictabilities. We provide a solution to disentangle the genuine relation between variables (the parameters linking them) from the unconventional dynamics that drive them. As an application, we show that GBP-USD forward premia have no predictive power for excess returns over 1976–2015 (thus solving this forward-premium puzzle) once the unconventional dynamics of spot rates are modeled. Taking advantage of these dynamics, we uncover a trading strategy which consistently outperforms existing ones in the out-of-sample period 2015–2021, delivering almost treble their profits and yielding a Sharpe ratio of 85%. Hence, even in this heavily traded market, the efficient market hypothesis has been failing for over 45 years as persistent profit opportunities remained unexploited because of the unconventional dynamics of the spot rate.