Handbook of Exchange Rates

8.5 Combined Forecasts

Our analysis has so far focused on evaluating the performance of individual empirical exchange rate models relative to the RW benchmark. Considering a large set of alternative models that capture different aspects of exchange rate behavior without knowing which model is “true” (or best) inevitably generates model uncertainty. In this section, we resolve this uncertainty by exploring whether portfolio performance improves when combining the forecasts arising from the full set of predictive regressions. Even though the potentially superior performance of combined forecasts is known since the seminal work of Bates and Granger (1969), applications in finance are only recently becoming increasingly popular (Timmermann, 2006). Rapach et al. (2010) argue that forecast combinations can deliver statistically and economically significant OOS gains for two reasons: (i) they reduce forecast volatility relative to individual forecasts and (ii) they are linked to the real economy.¹⁵

Recall that we estimate N = 6 predictive regressions, each of which provides an individual forecast for the one-step-ahead exchange rate return, where i ≤ N. We define the combined forecast as the weighted average of the N individual forecasts :

8.25

where are the ex-ante combining weights ...