Forecasting groups of time series is of increasing practical importance, e.g. forecasting the demand for multiple products offered by a retailer or server loads within a data center. The local approach to this problem considers each time series separately and fits a function or model to each series. The global approach fits a single function to all series. For groups of similar time series, global methods outperform the more established local methods. However, recent results show good performance of global models even in heterogeneous datasets. 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 and global methods, we provide the following contributions: 1) Global methods are not more restrictive than local methods, both can produce the same forecasts without any assumptions about similarity of the series. Global models can succeed in a wider range of problems than previously thought. 2) Basic generalization bounds for local and global algorithms. The complexity of local methods grows with the size of the set while it remains constant for global methods. In large datasets, a global algorithm can afford to be quite complex and still benefit from better generalization. These bounds serve to clarify and support recent experimental results in the field, and guide 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 from these principles, such as global linear models or deep networks result in superior accuracy. In particular, global linear models can provide competitive accuracy with two orders of magnitude fewer parameters than local methods.
翻译:预测时间序列组具有越来越大的实际重要性,例如,预测零售商或服务器在数据中心内装载的货物对多种产品的需求。 这一问题的当地方法将每个时间序列分开考虑,每个序列的功能或模式都适合。 全球方法适合所有序列的单一功能。 对于类似时间序列组,全球方法优于较老化的当地方法。 然而,最近的结果显示,全球模型的性能,即使是在混杂的数据集中也是如此。这表明全球方法的可适用性更加普遍,可能导致更准确的工具和新情景研究。用本地和全球方法正式确定一套时间序列的预测,我们提供以下贡献:(1) 全球方法并不比本地方法更具限制性,而且适合每个系列的功能或模式。对于类似时间序列的任何假设,全球方法都符合相同的单一功能。全球模型可以在比以前想象的更广泛的一系列问题上取得成功。 本地方法的复杂性随着成套方法的大小而增加,而全球方法则比全球方法的稳定性要低。 在大型数据集中,全球算算算得更复杂、更精确的时间序列序列序列序列, 在更精确的最近的全球历史级模型中,这些必然的结果是更精确的。