Bayesian Forecasting of Many Count-Valued Time Series
开发了针对非负计数时间序列的动态模型预测方法，结合贝叶斯分析实现快速并行处理，并通过多尺度方法实现跨序列信息共享，主要应用于超市销售预测。
This paper develops forecasting methodology and application of new classes of dynamic models for time series of non-negative counts. Novel univariate models synthesise dynamic generalized linear models for binary and conditionally Poisson time series, with dynamic random effects for over-dispersion. These models allow use of dynamic covariates in both binary and non-zero 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 multi-scale 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, hence enables scalability in the number of series. The major motivating context is supermarket sales forecasting. Detailed examples drawn from a case study in multi-step forecasting of sales of a number of related items showcase forecasting of multiple series, with discussion of forecast accuracy metrics and broader questions of probabilistic forecast accuracy assessment.