Reconciling Random Walks and Predictability: A Dual- Component Model of Exchange Rate Dynamics

This paper addresses a key puzzle in international finance: whether exchange rates follow a random walk or exhibit predictable patterns. We demonstrate that exchange rates can possess a unit root while maintaining substantial predictability over certain horizons. Our model combines a stochastic trend—representing the slowly moving equilibrium exchange rate—and a stationary cyclical component capturing temporary deviations, reconciling long-term random walk behavior with medium-term predictability. This dual-component framework is essential for capturing three key features of exchange rate dynamics: expected exchange rate changes are not zero, they are highly persistent, and there is a strong relationship between exchange rate levels and expected future changes. Without the stationary component, expected exchange rate changes would be zero, and if the stochastic trend evolved too quickly, this relationship would break down. To illustrate, we extend the Bacchetta and van Wincoop (2021) framework (which generates a stationary component of the exchange rate) with a stochastic trend. Our model generates an inverted U-shaped pattern where forecast accuracy peaks at intermediate horizons and predicts that multi-year exchange rate changes are increasing multiples of one-year changes. Using data from 2000–2024 for nine inflation-targeting countries with freely floating exchange rates, we find strong empirical support for these predictions, with our model consistently outperforming the random walk benchmark in out-of-sample tests.