Quantile autoregressive moving average models for ratio-based bounded time series

2026-05-25

AI Summary

This study addresses the limitations of traditional mean-based modeling approaches for proportion-valued time series confined to the open interval (0,1), which often exhibit asymmetry, heavy tails, and dynamic conditional quantile behavior. To overcome these challenges, the authors propose the QULS-ARMA model, which innovatively embeds an ARMA structure within the conditional quantile function of the unit-log-symmetric (ULS) distribution family. By employing quantile reparameterization, this framework establishes a novel paradigm for modeling bounded proportional data that transcends conventional mean regression, offering flexible characterization of distributional shape. The paper develops asymptotic theory based on conditional maximum likelihood estimation and demonstrates through Monte Carlo simulations that the estimators exhibit favorable finite-sample performance across various kernel specifications. Empirical application to Brazilian hydroelectric reservoir storage proportions confirms the model’s practical efficacy and advantages.

Abstract

This paper proposes the quantile unit-log-symmetric autoregressive moving average (QULS--ARMA) model for bounded time series on the open unit interval $(0,1)$. The model extends the unit-log-symmetric family by introducing a quantile-based reparameterization and embedding autoregressive and moving-average dynamics directly in the conditional quantile, thereby overcoming limitations of mean-based approaches and providing a coherent framework for proportion data arising from ratios of dependent positive variables. The proposed specification accommodates asymmetric behavior and heavy tails through flexible log-symmetric kernels, including the normal and Student-$t$ distributions. Parameter estimation is carried out via conditional maximum likelihood, and asymptotic properties are established. Monte Carlo simulations and an empirical application to hydroelectric energy storage proportions in Brazil assess the finite-sample performance and practical advantages of the QULS--ARMA model. The results show the good performance of the proposed estimators across a range of scenarios and kernel specifications.

Problem

• bounded time series
• quantile modeling
• proportion data
• asymmetric behavior
• heavy tails

Innovation

• quantile regression
• unit-log-symmetric distribution
• ARMA model
• bounded time series
• conditional maximum likelihood