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Forecasting groups of time series is of increasing practical importance, e.g.forecasting the demand for multiple products offered by a retailer or serverloads within a data center. The local approach to this problem considers eachtime series separately and fits a function or model to each series. The globalapproach fits a single function to all series. For groups of similar timeseries, global methods outperform the more established local methods. However,recent results show good performance of global models even in heterogeneousdatasets. This suggests a more general applicability of global methods,potentially leading to more accurate tools and new scenarios to study.  Formalizing the setting of forecasting a set of time series with local andglobal methods, we provide the following contributions:  1) Global methods are not more restrictive than local methods, both canproduce the same forecasts without any assumptions about similarity of theseries. Global models can succeed in a wider range of problems than previouslythought.  2) Basic generalization bounds for local and global algorithms. Thecomplexity of local methods grows with the size of the set while it remainsconstant for global methods. In large datasets, a global algorithm can affordto be quite complex and still benefit from better generalization. These boundsserve to clarify and support recent experimental results in the field, andguide the design of new algorithms. For the class of autoregressive models,this implies that global models can have much larger memory than local methods.  3) In an extensive empirical study, purposely naive algorithms derived fromthese principles, such as global linear models or deep networks result insuperior accuracy.  In particular, global linear models can provide competitive accuracy with twoorders of magnitude fewer parameters than local methods.

Principles and Algorithms for Forecasting Groups of Time Series: Locality and Globality