🤖 AI Summary
Existing open-source tools struggle to efficiently support dynamic quantile regression modeling and uncertainty quantification, particularly in time series contexts. This work proposes the R package exdqlm, which establishes a unified framework for dynamic quantile linear models based on the extended asymmetric Laplace distribution. The framework accommodates both static and dynamic specifications and incorporates regularized priors, transition functions, and cross-quantile posterior predictive synthesis. By integrating MCMC with a fast Laplace–delta variational Bayesian inference scheme, the method substantially enhances computational efficiency for long time series while preserving the accuracy of uncertainty quantification. The resulting tool enables efficient modeling, precise forecasting, and comprehensive diagnostic capabilities, thereby addressing a critical gap in practical implementations of complex time series quantile regression analysis.
📝 Abstract
We present the R package exdqlm for Bayesian quantile regression, with primary emphasis on dynamic state-space quantile models for time series. The package is built around extended dynamic quantile linear models (exDQLMs), which use the extended asymmetric Laplace (exAL) family, a parametric extension of the asymmetric Laplace (AL) distribution commonly used in quantile regression. The software provides posterior simulation via Markov chain Monte Carlo (MCMC) and fast approximate posterior inference via Laplace-delta variational Bayes (LDVB), supporting posterior uncertainty quantification while also providing a computationally efficient option for longer time series. The same package interface supports static exAL quantile regression with regularized priors, dynamic transfer-function models for nonlinear input effects at a given quantile, post hoc posterior-predictive synthesis across separately fitted quantiles, forecasting, and quantitative and visual diagnostics for model evaluation.