Abstract

We develop and exemplify application of new classes of dynamic models for time series of nonnegative counts. Our novel univariate models combine dynamic generalized linear models for binary and conditionally Poisson time series, with dynamic random effects for over-dispersion. These models estimate dynamic regression coefficients in both binary and nonzero count components. Sequential Bayesian analysis allows fast, parallel analysis of sets of decoupled time series. New multivariate models then enable information sharing in contexts when data at a more highly aggregated level provide more incisive inferences on shared patterns such as trends and seasonality. A novel multiscale approach—one new example of the concept of decouple/recouple in time series—enables information sharing across series. This incorporates cross-series linkages while insulating parallel estimation of univariate models, and hence enables scalability in the number of series. The major motivating context is supermarket sales forecasting. Detailed examples drawn from a case study in multistep forecasting of sales of a number of related items showcase forecasting of multiple series, with discussion of forecast accuracy metrics, comparisons with existing methods, and broader questions of probabilistic forecast assessment.

摘要

我们为非负计数的时间序列开发并举例说明了新类别的动态模型的应用。我们新颖的单变量模型将针对二进制和有条件泊松时间序列的动态广义线性模型与针对超分散的动态随机效应结合在一起。这些模型估计二进制和非零计数分量中的动态回归系数。顺序贝叶斯分析允许快速，并行地分析解耦时间序列集。然后，当更高聚合级别的数据对共享模式（例如趋势和季节性）提供更敏锐的推断时，新的多元模型就可以在上下文中实现信息共享。一种新颖的多尺度方法（时间序列解耦/重新耦合概念的一个新示例）使跨序列的信息共享成为可能。这合并了交叉系列链接，同时隔离了单变量模型的并行估计，因此可以实现系列数量的可伸缩性。主要的推动因素是超市销售预测。从对多个相关项目的销售进行多步预测的案例研究中获得的详细示例展示了对多个系列的预测，并讨论了预测准确性指标，与现有方法的比较以及更广泛的概率预测评估问题。