This dissertation consists of three chapters. Collectively they attempt to investigate

on how to better forecast a time series variable when there is uncertainty on the stability

of model parameters.

The first chapter applies the newly developed theory of optimal and robust weights

to forecasting the U.S. market equity premium in the presence of structural breaks.

The empirical results suggest that parameter instability cannot fully explain the weak

forecasting performance of most predictors used in related empirical research.

The second chapter introduces a two-stage forecast combination method to forecasting

the U.S. market equity premium out-of-sample. In the first stage, for each predictive

model, we combine its stable and break cases by using several model averaging methods. Next, we pool all adjusted predictive models together by applying equal weights. The empirical results suggest that this new method can potentially offer substantial predictive gains relative to the simple one-stage overall equal weights method.

The third chapter extends model averaging theory under uncertainty regarding structural

breaks to the out-of-sample forecast setting, and proposes new predictive model

weights based on the leave-one-out cross-validation criterion (CV), as CV is robust to

heteroscedasticity and can be applied generally. It provides Monte Carlo and empirical

evidence showing that CV weights outperform several competing methods.