Over the past decades developed market exchange rates have displayed two important regularities. First, real exchange rates (nominal exchange rates adjusted for domestic price trends) have been mean reverting. Second, the mean reversion has predominantly come in form of nominal exchange rate trends. Hence, a simple rule of thumb for exchange rate trends can be based on the expected re-alignment the real exchange rates with long-term averages over 2-5 years. According to a new paper, FX trend forecasting models based on this rule outperform both the random walk and more complex forecasting models.

*The post ties in with SRSV’s lecture on macro trend indicators, particularly the section on macroeconomic indicators and long-term market trends.
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*The below are excerpts from the paper. Emphasis and cursive text have been added.*

### Empirical regularities

“The international finance literature has documented two important regularities in foreign exchange markets. First…for developed countries, __real exchange rates are reverting to the level implied by the Purchasing Power Parity theory__. Second, __for flexible currency regimes the adjustment process is mainly driven by the nominal exchange rate__.”

“Real exchange rates are mean reverting over medium-term horizons. A particularly neat way to illustrate this is to scatter plot changes of real bilateral exchange rate of the euro at different horizons relative to its starting level. The negative correlation, already visible at the six-month, gets progressively stronger at longer horizons, proving that there is a powerful self-adjusting mechanism at play. The __second regularity is illustrated by the middle and bottom panels of [ the figure below], which show very clearly how the nominal exchange rate and not the relative rice index drives this adjustment process__. This stylized fact is entirely intuitive, if we think that NERs play an important role in absorbing atypical movements in price competitiveness.”

“Particularly remarkable is how robust these results are to all currency pairs in our dataset.”

“The above in-sample analysis suggests that real and nominal exchange rates do not behave like random walks…[*and*] highlights also that __equilibrium exchange rate analysis matters__. Simple measures of exchange rate disequilibria not only signal economic imbalances but also provide hints in which direction the exchange rate will go.”

### Predicting exchange rate trends

“The two above in-sample regularities of foreign exchange markets can be exploited to __infer out-of-sample movements of major currency pairs__…From the IMF-IFS and BIS databases we have taken monthly end-of-period nominal exchange rates against the USD and consumer price index (CPI) data over the period 1975:1-2017:5 for the following countries: Australia (AUD), Canada (CAD), Japan (JPY), New Zealand (NZD), Switzerland (CHF), the United Kingdom (GBP), the euro area (EUR), Korea (KRW), Norway (NOK), Sweden, (SEK) and the United States (US).”

“We…evaluate a battery of models that aim to exploit [*empirical*] regularities for forecasting purposes. __The winner of the forecasting race is a calibrated PPP model, which just assumes that the real exchange rate gradually returns to its sample mean__, completing half of the adjustment in 3 years, and that the adjustment is only driven by the nominal exchange rate. This __approach is so simple that it can be implemented even on the back of a napkin __in two steps. Step 1 consists in calculating the initial real exchange rate misalignment with an eyeball estimate of what is the distance from the sample mean. Step 2 consists in recalling that, according to this model, one tenth of the required adjustment is achieved by the nominal exchange rate in the first 6 months, one fifth in one year, just over a third in two years and exactly half after 3 years.”

“Calibrating the half-life real exchange rate adjustment to three years and assuming a random walk for relative price indices is, at least for advanced countries, a simpler and generally better option than forecasting the nominal exchange rate with the random walk or relying on estimated models.”

### The case for simplicity

“Although so easy to compute, __such projections [ as shown above] are much more accurate than those derived with complex time series models__…Simple variants of this approach, by changing the calibration of the half-life adjustment within reasonable values (i.e. between 2 and 5 years) or changing the methodology for calculating the real exchange rate equilibrium would, in general, not change the outcome qualitatively.”

“__Severe problems arise when attempting to carry out more sophisticated approaches,__ such as estimating the pace of mean reversion of the real exchange rate or forecasting relative inflation. Among the estimated approaches, we find that it is strongly preferable to rely on direct rather than multi-step iterative forecasting methods.”

“Previous studies, which relied on estimated models, could not systematically beat the random walk in light of the pervasive role of the forecast error attributed to estimation… Among the estimated approaches, it is clearly better to rely on ‘direct’ rather than ‘multi-step iterative’ forecasting techniques.”