Sunday, January 12, 2025

Random walk and exchange rate predictability - trend with mean-reversion



A recent paper, "Reconciling Random Walks and Predictability: A Dual-Component Model of Exchange Rate Dynamics", provides some interesting insight on the time series properties of exchange rates. The paper finds that exchange rates have a unit root but there also is predictability at different time horizons.  This seems odd given the history of exchange rates which suggests that they are hard to predict, and that a random walk is the most effective prediction. 

The model presented combines a stochastic trend which represents the slow-moving change in equilibrium exchange rates with a stationary cyclical component that captures the temporary deviations from the long-term equilibrium. This model shows that expected exchange rate changes are not zero and persistent and there is a strong relationship between exchange rate levels and expected future changes. This may not help with forecasting in the short run, but it does suggest that there are systematic changes in exchange rates that can result in predictable moves over a random walk. 

There is hope for exchange rate forecasting. Now, for many forecasters and traders this support their thinking, but the important part of this paper is that there are two key components, a long-term trend which is based on fundamentals and a cyclical component that suggests mean-reversion to the long-term trend. Always think of exchange rates as this two-component model.



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