The present work introduces a new model class for continuous random variables that have support in the positive real line. This model is designed to explain conditional quantiles and provides an alternative approach for modeling data with asymmetric behavior. Specifically, we present a novel autoregressive moving average model based on the \(\tau \) -th quantile of the Burr XII distribution. The advantage of using the quantile is that it is less sensitive to heterogeneous populations and more robust in the presence of outliers than the average. Our proposed model enables the dynamic modeling of any quantile through a structured approach incorporating autoregressive terms, moving averages, time-varying regressors, and a link function. We adopt the conditional maximum likelihood method to estimate the model parameters and construct confidence intervals. Furthermore, we assess the performance of the proposed model’s parameter estimators through Monte Carlo simulations. We also demonstrate the model’s usefulness through diagnostic tools and empirical applications on two datasets related to the financial market and the environment. Furthermore, we also compare the new model’s performance to that of competing models.
