Bayesian forecasting of many count-valued time series

TL;DR

This paper introduces new Bayesian dynamic models for forecasting multiple count-valued time series, enabling scalable, multi-scale analysis with information sharing across series, demonstrated through supermarket sales case studies.

Contribution

It develops novel univariate and multivariate Bayesian models for count data, incorporating dynamic covariates, over-dispersion, and a multi-scale approach for scalable, shared inference across many series.

Findings

Models effectively forecast supermarket sales data.

Sequential Bayesian analysis enables fast, parallel processing.

Multi-scale approach improves inference on shared patterns.

Abstract

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.