UCSC-SOE-21-10: exdqlm: An R Package for Estimation and Analysis of Flexible Dynamic Quantile Linear Models

Raquel Barata, Raquel Prado and Bruno Sanso
08/12/2021 02:56 PM
We present the R package exdqlm as a tool for dynamic quantile regression. The main focus of the package is to provide a framework for Bayesian inference and forecasting of flexible dynamic quantile linear models (exDQLMs). exDQLMs utilize a new family of error distributions for parametric quantile regression, the extended asymmetric Laplace (exAL), a generalization of the asymmetric Laplace (AL) which is commonly used in parametric quantile regression. Estimation of a dynamic quantile linear model, which utilizes the AL, is included in the package as a special case. Non-time-varying quantile regression models are also a special case of our methods. Further, routines for estimation of a nonlinear relationship between the response and a given input variable at a specified quantile via a transfer function model are available. The software provides the choice of two different algorithms for posterior inference: Markov chain Monte Carlo (MCMC), and importance sampling variational Bayes (ISVB). While MCMC provides an efficient sample-based exploration of the posterior distribution, the approximation obtained by the ISVB algorithm enables fast inference for long time series at a fraction of the memory and computational costs of the MCMC. A routine for forecasting the dynamic quantile is available in the package, as well as several quantitative and visual diagnostics for model evaluation. We illustrate the implementation of the functions and algorithms in the exdqlm package with a step-by-step guide for the analysis of several real data sets.