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In the current context of Big Data, the nature of many forecasting problems has changed from predicting isolated time series to predicting many time series from similar sources. This has opened up the opportunity to develop competitive global forecasting models that simultaneously learn from many time series. But, it still remains unclear when global forecasting models can outperform the univariate benchmarks, especially along the dimensions of the homogeneity/heterogeneity of series, the complexity of patterns in the series, the complexity of forecasting models, and the lengths/number of series. Our study attempts to address this problem through investigating the effect from these factors, by simulating a number of datasets that have controllable time series characteristics. Specifically, we simulate time series from simple data generating processes (DGP), such as Auto Regressive (AR) and Seasonal AR, to complex DGPs, such as Chaotic Logistic Map, Self-Exciting Threshold Auto-Regressive, and Mackey-Glass Equations. The data heterogeneity is introduced by mixing time series generated from several DGPs into a single dataset. The lengths and the number of series in the dataset are varied in different scenarios. We perform experiments on these datasets using global forecasting models including Recurrent Neural Networks (RNN), Feed-Forward Neural Networks, Pooled Regression (PR) models and Light Gradient Boosting Models (LGBM), and compare their performance against standard statistical univariate forecasting techniques. Our experiments demonstrate that when trained as global forecasting models, techniques such as RNNs and LGBMs, which have complex non-linear modelling capabilities, are competitive methods in general under challenging forecasting scenarios such as series having short lengths, datasets with heterogeneous series and having minimal prior knowledge of the patterns of the series.