Accurate forecasts about the future are vital in time series analyses, but accurately modeling complex structures in the data is always challenging. Two major sources of complexity are autoregressive conditional heteroskedasticity (ARCH) effects on data as well as structural breaks in the data, as these affect the quality of data and hence reduce forecast accuracy. In this regard, combining forecast types has been a helpful strategy for improving forecast accuracy for more than 50 years since Bates and Granger's (1969) original paper. Hence, this paper aims to examine if the gains from combined forecasts are sustained regarding cases with structural breaks and ARCH innovations. Moreover, the study explores which forecast combination schemes are optimal for those cases by combining the exponential smoothing (ETS), autoregressive integrated moving average (ARIMA), and artificial neural network (ANN) forecast models using simple and regression-based combination procedures. These methods are implemented in both simulated series and over empirical data from two popular Turkish stock exchanges (i.e., BIST-30 and BIST-100 Indexes). The study has found regressionbased forecast combination methods to significantly improve forecast accuracy regarding cases with structural breaks and conditional heteroscedasticity. Dynamically weighted combinations show greater accuracy improvement compared to their static counterparts when the data contain a trend. Simple combination schemes, including simple averages, just perform better than single methods for ETS and ARIMA, while they barely outperform ANN. In conclusion, ANN is found to be the best-performing individual forecasting method for all cases and designs.