Browsing by Subject "Bayesian forecasting"

Problems of forecasting related time series of counts arise in a diverse array of applications such as consumer sales, epidemiology, ecology, law enforcement, and tourism. Characteristics of high-frequency count data including many zeros, high variation, extreme values, and varying means make the application of traditional time series methods inappropriate. In many settings, an additional challenge is producing on-line, multi-step forecasts for thousands of individual series in an efficient and flexible manner. This dissertation introduces novel classes of models to address efficiency, efficacy and scalability of dynamic models based on the concept of decouple/recouple applied to multiple series that are individually represented via novel univariate state-space models. The novel dynamic count mixture model involves dynamic generalized linear models for binary and conditionally Poisson time series, with dynamic random effects for overdispersion, and the use of dynamic covariates in both binary and non-zero components. New multivariate models then enable information sharing in contexts where data at a more highly aggregated level provide more incisive inference on shared patterns such as trends and seasonality. This novel decouple/recouple strategy incorporates cross-series linkages while insulating parallel estimation of univariate models. We extend these models to a general framework appropriate for settings in which count data arises through a compound process. The motivating application is in consumer sales contexts where variability in high-frequency sales data arises from the compounding effects of the number of transactions and the number of sales-per-transactions. This framework involves adapting the dynamic count mixture model to forecast transactions, coupled with a binary cascade concept using a sequence of Bayesian models to predict the number of units per transaction. The motivation behind the binary cascade is that the appropriate way to model rare events is through a sequence of conditional probabilities of increasingly rare outcomes. Several case studies in many-item, multi-step ahead supermarket sales forecasting demonstrate improved forecasting performance using the proposed models, with discussion of forecast accuracy metrics and the benefits of probabilistic forecast accuracy assessment.

This thesis discusses novel developments in Bayesian analytics for high-dimensional multivariate time series. The focus is on the class of multiregression dynamic models (MDMs), which can be decomposed into sets of univariate models processed in parallel yet coupled for forecasting and decision making. Parallel processing greatly speeds up the computations and vastly expands the range of time series to which the analysis can be applied.

I begin by defining a new sparse representation of the dependence between the components of a multivariate time series. Using this representation, innovations involve sparse dynamic dependence networks, idiosyncrasies in time-varying auto-regressive lag structures, and flexibility of discounting methods for stochastic volatilities.

For exploration of the model space, I define a variant of the Shotgun Stochastic Search (SSS) algorithm. Under the parallelizable framework, this new SSS algorithm allows the stochastic search to move in each dimension simultaneously at each iteration, and thus it moves much faster to high probability regions of model space than does traditional SSS.

For the assessment of model uncertainty in MDMs, I propose an innovative method that converts model uncertainties from the multivariate context to the univariate context using Bayesian Model Averaging and power discounting techniques. I show that this approach can succeed in effectively capturing time-varying model uncertainties on various model parameters, while also identifying practically superior predictive and lucrative models in financial studies.

Finally I introduce common state coupled DLMs/MDMs (CSCDLMs/CSCMDMs), a new class of models for multivariate time series. These models are related to the established class of dynamic linear models, but include both common and series-specific state vectors and incorporate multivariate stochastic volatility. Bayesian analytics are developed including sequential updating, using a novel forward-filtering-backward-sampling scheme. Online and analytic learning of observation variances is achieved by an approximation method using variance discounting. This method results in faster computation for sequential step-ahead forecasting than MCMC, satisfying the requirement of speed for real-world applications.

A motivating example is the problem of short-term prediction of electricity demand in a "Smart Grid" scenario. Previous models do not enable either time-varying, correlated structure or online learning of the covariance structure of the state and observational evolution noise vectors. I address these issues by using a CSCMDM and applying a variance discounting method for learning correlation structure. Experimental results on a real data set, including comparisons with previous models, validate the effectiveness of the new framework.

The combination of forecast densities, whether they result from a set of models,

a group of consulted experts, or other sources, is becoming increasingly important

in the fields of economics, policy, and finance, among others. Requiring methodology

that goes beyond standard Bayesian model uncertainty and model mixing -

with its well-known limitations based on a clearly proscribed theoretical basis - multiple

`density combination' methods have been proposed. While some proposals have

demonstrated empirical success, most apparently lack a core philosophical and theoretical

foundation. Interesting recent examples generalize the common `linear opinion

pool' with

flexible mixing weights that depend on the forecast variable itself -

i.e., outcome-dependent mixing. This dissertation takes a foundational subjective

Bayesian perspective in order to show that such a density combination scheme is

in fact justified as one example of Bayesian agent opinion analysis, or `predictive

synthesis'. This logically coherent framework clearly delineates the underlying assumptions

as well as the theoretical constraints and limitations of many combination

`rules', defining a broad class of Bayesian models for the general problem. A number

of examples, including applications to sets of predictive densities for foreign exchange

and United States inflation time series data, provide illustrations.

Chapters 1-2 introduce and describe the ideas involved in Bayesian predictive

synthesis (BPS) as a method of subjective analysis. Chapters 3-4 describe different

possible formulations of outcome-dependent mixing. Chapter 5 places the analysis into a time series context and covers relevant inference techniques. Chapters 6 and 7

apply the time series analysis to euro currency forecasts and United States inflation

data. Chapter 8 concludes.

This thesis addresses the financial econometric problem of forecasting the term structure of interest rates by using classes of Dynamic Dependence Network Models (DDNMs). This Bayesian econometric framework defines structured dynamic graphical models for multivariate time series that utilize a hierarchical, contemporaneous dependence structure across series augmented with time-varying autoregressive components. Using yield and macroeconomic data from the post-Volcker era, various such models are explored and evaluated. On the basis of economic reasoning and empirical statistical evaluations, we specify an interpretable model which outperforms a standard time-varying vector autoregressive model in forecast accuracy particularly at longer horizons relevant for economic policy considerations. In particular, the chosen model reduces forecast error metrics and produces stable forecast trajectories for yields on U.S. Treasuries up to 12 months ahead. The out-of-sample performance of the DDNM is robust to changes in model specification, hyper-parameter choices, and exogenous macroeconomic information sets. The analysis highlights the utility of this class of models and suggests next steps in research and development in this area of Bayesian macroeconomics.