Many researchers have argued that combining many models for forecasting gives better estimates than single time series models. For example, a hybrid architecture comprising an autoregressive integrated moving average model (ARIMA)and a neural network is a well-known technique that has recently been shown to give better forecasts by taking advantage of each model’s capabilities. However, this assumption carries the danger of underestimating the relationship between the model’s linear and non-linear components, particularly by assuming that individual forecasting techniques are appropriate, say, for modeling the residuals. In this paper, we show that such combinations do not necessarily outperform individual forecasts. On the contrary, we show that the combined forecast can underperform significantly compared to its constituents’ performances. We demonstrate this using nine data sets, autoregressive linear and time-delay neural network models.