Bayesian Approaches for Forecasting Count-Valued Time Series
| dc.contributor.advisor | Kowal, Daniel R | |
| dc.creator | King, Brian | |
| dc.date.accessioned | 2023-08-09T19:15:07Z | |
| dc.date.available | 2023-08-09T19:15:07Z | |
| dc.date.created | 2023-05 | |
| dc.date.issued | 2023-04-18 | |
| dc.date.submitted | May 2023 | |
| dc.date.updated | 2023-08-09T19:15:07Z | |
| dc.description.abstract | This thesis introduces novel Bayesian approaches to modeling and forecasting count-valued time series, particularly emphasizing the importance of distributional forecasting and proper, data-coherent uncertainty quantification. Time-ordered count data arise in many applications, including sales, finance, ecology, and epidemiology/public health. Such data exhibit a variety of complexities that make modeling difficult: they often inherit typical time series characteristics such as seasonality or high frequency, but also present numerous distributional features unique to the count setting, like zero-inflation, over-/under-dispersion, and heaping. Importantly, these count data features can rarely be summarized by a point estimate or even interval estimates. Instead, there is a pressing need for methods that can forecast entire distributions and allow decision makers access to uncertainty quantification built for the count data setting. In the first project, we introduce a broad class of multivariate state space models called the warped Dynamic Linear Model (warpDLM). Through a warping operation composed of a transformation function and rounding operator, the warpDLM connects count data to latent continuous data that can be modeled with a DLM. Thus, our model adapts the powerful existing methods for time series data in a way that allows for modeling the many complexities of count data. We develop conjugate inference for the warpDLM, which enables analytic and recursive updates, in turn facilitating the development of efficient algorithms for inference and forecasting, including Monte Carlo simulation for offline analysis and an optimal particle filter for online inference. The forecasting ability of this framework is demonstrated on simulated data as well as a real-data application of EMS calls regarding overdoses in the city of Cincinnati. In the second project, we take a different approach to the forecasting problem. Instead of training a model suited for count time series, we consider the scenario where several point forecasts for a count time series are available and explore how these could be combined to output a calibrated probabilistic forecast. To accomplish this task, we leverage a flexible Bayesian count regression model which (akin to the warpDLM) performs Simultaneous Transformation and Rounding (STAR) of a latent continuous regression model. The resulting forecast combination approach (called STARcast) can produce calibrated and sharp distributional forecasts, even with only a small collection of point forecasts as the input. The third project introduces a statistical software package, countSTAR, designed for both practitioners and researchers to utilize the methods proposed in this thesis, alongside many additional STAR models explored in other works. In addition to including functionality for warpDLM modeling, countSTAR features unified syntax, useful output, and detailed online documentation. This package has been accepted to CRAN, and thus is free and easily available to R users. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.citation | King, Brian. "Bayesian Approaches for Forecasting Count-Valued Time Series." (2023) Diss., Rice University. <a href="https://hdl.handle.net/1911/115172">https://hdl.handle.net/1911/115172</a>. | |
| dc.identifier.uri | https://hdl.handle.net/1911/115172 | |
| dc.language.iso | eng | |
| dc.rights | Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. | |
| dc.subject | count data | |
| dc.subject | probabilistic forecasting | |
| dc.subject | state space models | |
| dc.subject | forecast combination | |
| dc.title | Bayesian Approaches for Forecasting Count-Valued Time Series | |
| dc.type | Thesis | |
| dc.type.material | Text | |
| thesis.degree.department | Statistics | |
| thesis.degree.discipline | Engineering | |
| thesis.degree.grantor | Rice University | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Doctor of Philosophy |
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