Dynamic generalized linear models for non-Gaussian time series forecasting

This paper introduces a novel sequential inferential approach for Bayesian dynamic generalized linear models, focusing on uni- or multivariate k-parametric exponential families, which handle various responses such as multinomial, gamma, normal, and Poisson. This approach preserves the sequential nature of Bayesian paradigm for generating real-time inferences, utilizing the conjugate structure of the exponential family for computational efficiency. The framework incorporates c...

This paper introduces kDGLM, an R package designed for Bayesian analysis of Generalized Dynamic Linear Models (GDLM), with a primary focus on both uni- and multivariate exponential families. Emphasizing sequential inference for time series data, the kDGLM package provides comprehensive support for fitting, smoothing, monitoring, and feed-forward interventions. The methodology employed by kDGLM, as proposed in Alves et al. (2024), seamlessly integrates with well-established te...

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 se...

We develop a Bayesian framework for estimation and prediction of dynamic models for observations from the two-parameter exponential family. Different link functions are introduced to model both the mean and the precision in the exponential family allowing the introduction of covariates and time series components. We explore conjugacy and analytical approximations under the class of partial specified models to keep the computation fast. The algorithm of West, Harrison and Migo...

Dynamic linear models with Gaussian observations and Gaussian states lead to closed-form formulas for posterior simulation. However, these closed-form formulas break down when the response or state evolution ceases to be Gaussian. Dynamic, generalized linear models exemplify a class of models for which this is the case, and include, amongst other models, dynamic binomial logistic regression and dynamic negative binomial regression. Finding and appraising posterior simulation ...

Dynamic linear models (DLM) offer a very generic framework to analyse time series data. Many classical time series models can be formulated as DLMs, including ARMA models and standard multiple linear regression models. The models can be seen as general regression models where the coefficients can vary in time. In addition, they allow for a state space representation and a formulation as hierarchical statistical models, which in turn is the key for efficient estimation by Kalm...

Inference for streaming time-series is tightly coupled with the problem of Bayesian on-line state and parameter inference. In this paper we will introduce Dynamic Generalised Linear Models, the class of models often chosen to model continuous and discrete time-series data. We will look at three different approaches which allow on-line estimation and analyse the results when applied to different real world datasets related to inference for streaming data. Sufficient statistics...

Detection and modeling of change-points in time-series can be considerably challenging. In this paper we approach this problem by incorporating the class of Dynamic Generalized Linear Models (DGLM) into the well know class of Product Partition Models (PPM). This new methodology, that we call DGLM-PPM, extends the PPM to distributions within the Exponential Family while also retaining the flexibility of the DGLM class. It also provides a framework for Bayesian multiple change-...

Bayesian computation for filtering and forecasting analysis is developed for a broad class of dynamic models. The ability to scale-up such analyses in non-Gaussian, nonlinear multivariate time series models is advanced through the introduction of a novel copula construction in sequential filtering of coupled sets of dynamic generalized linear models. The new copula approach is integrated into recently introduced multiscale models in which univariate time series are coupled vi...

Generalized autoregressive moving average (GARMA) models are a class of models that was developed for extending the univariate Gaussian ARMA time series model to a flexible observation-driven model for non-Gaussian time series data. This work presents Bayesian approach for GARMA models with Poisson, binomial and negative binomial distributions. A simulation study was carried out to investigate the performance of Bayesian estimation and Bayesian model selection criteria. Also ...