Principles and algorithms for forecasting groups of time series: locality and globality

Global methods that fit a single forecasting method to all time series in a set have recently shown surprising accuracy, even when forecasting large groups of heterogeneous time series. We provide the following contributions that help understand the potential and applicability of global methods and how they relate to traditional local methods that fit a separate forecasting method to each series: • Global and local methods can produce the same forecasts without any assumptions about similarity of the series in the set. • The complexity of local methods grows with the size of the set while it remains constant for global methods. This result supports the recent evidence and provides principles for the design of new algorithms. • In an extensive empirical study, we show that purposely naïve algorithms derived from these principles show outstanding accuracy. In particular, global linear models provide competitive accuracy with far fewer parameters than the simplest of local methods.