Bayesian Computation for Variable Selection and Multivariate Forecasting in Dynamic Models

Challenges arise in time series analysis due to the need for sequential forecasting and updating of model parameters as data is observed. This dissertation presents techniques for efficient Bayesian computation in multivariate time series analysis. Computational scalability is a core focus of this work, and often rests on the decouple-recouple concept in which multivariate models are decoupled into univariate models for efficient inference, and then recoupled to produce joint forecasts. The first section of this dissertation develops novel methods for variable selection in which models are scored and weighted based on specific forecasting and decision goals. In the time series setting, standard marginal likelihoods correspond to 1−step forecast densities, and considering alternate objectives is shown to improve long-term forecast accuracy. Scoring models based on forecast objectives can be computationally intensive, so the model space is reduced by evaluating univariate models separately along each dimension. This enables an efficient search over large, higher dimensional model spaces. A second area of focus in this dissertation is product demand forecasting, driven by applied considerations in grocery store sales. A novel copula model is developed for multivariate forecasting with Dynamic Generalized Linear Models (DGLMs), with a variational Bayes strategy for inference in latent factor DGLMs. Three applied case studies demonstrate that these techniques increase computational efficiency by several orders of magnitude over comparable multivariate models, without any loss of forecast accuracy. An additional area of interest in product demand forecasting is the effect of holidays and special events. An error correction model is introduced for this context, demonstrating strong predictive performance across a variety of holidays and retail item categories. Finally, a new Python package for Bayesian DGLM analysis, PyBATS, provides a set of tools for user-friendly analysis of univariate and multivariate time series.