Forecasting groups of time series is of increasing practical importance, e.g.\nforecasting the demand for multiple products offered by a retailer or server\nloads within a data center. The local approach to this problem considers each\ntime series separately and fits a function or model to each series. The global\napproach fits a single function to all series. For groups of similar time\nseries, global methods outperform the more established local methods. However,\nrecent results show good performance of global models even in heterogeneous\ndatasets. This suggests a more general applicability of global methods,\npotentially leading to more accurate tools and new scenarios to study.\n Formalizing the setting of forecasting a set of time series with local and\nglobal methods, we provide the following contributions:\n 1) Global methods are not more restrictive than local methods, both can\nproduce the same forecasts without any assumptions about similarity of the\nseries. Global models can succeed in a wider range of problems than previously\nthought.\n 2) Basic generalization bounds for local and global algorithms. The\ncomplexity of local methods grows with the size of the set while it remains\nconstant for global methods. In large datasets, a global algorithm can afford\nto be quite complex and still benefit from better generalization. These bounds\nserve to clarify and support recent experimental results in the field, and\nguide the design of new algorithms. For the class of autoregressive models,\nthis implies that global models can have much larger memory than local methods.\n 3) In an extensive empirical study, purposely naive algorithms derived from\nthese principles, such as global linear models or deep networks result in\nsuperior accuracy.\n In particular, global linear models can provide competitive accuracy with two\norders of magnitude fewer parameters than local methods.\n