This thesis contributes to the literature of forecasting under structural breaks. Following the framework of Inoue, Jin, and Rossi (2017), Chapter 1 develops two window selection methods to select the optimal estimation sample size in rolling regressions in the presence of structural breaks and the Monte-Carlo experiments show the proposed bootstrap method is very competitive against existing methods, which could be a useful tool for practitioners. Chapter 2 applies the window selection methods

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... on forecasting exchange rates, where the forecasting devices beat the random walk benchmark in 7 out of 18 countries, but none of the devices or models perform consistently across countries. While the window selection methods could solve the "Meese-Rogoff" puzzle in a few countries, the fixed rolling window is preferred in most cases. The findings also suggest Mark's (1995) monetary model is the most promising model for exchange rate forecasting in the short horizon, rather than the Taylor rule fundamentals or PPP models. Chapter 3 provides strong evidence that parameter instability could result in forecast failure on linear models with a large set of Monte-Carlo experiments. It demonstrates that the linear forecasting models are more likely to fail when there are fewer observations available in the estimation sample, when making forecasts in the longer horizon, and when the external regressor is more volatile than the variable of interest. Moreover, the forecast failure is more likely to happen if the break date is closer to the forecasting date, if the variable of interest and the external regressor are both strongly autocorrelated, and if the parameter shift is negative instead of positive. Combining the findings in Chapter 2, it also implies that the flexible-price and sticky-rice monetary model could not be the true model of exchange rate movements.