Regression models based on the log-symmetric family of distributions are particularly useful when the response variable is continuous, positive, and asymmetrically distributed. In this article, we propose and derive a class of models based on a new approach to quantile regression using log-symmetric distributions parameterized by means of their quantiles. Two Monte Carlo simulation studies are conducted utilizing the R software.The first one analyzes the performance of the maximum likelihood estimators, the Akaike, Bayesian, and corrected Akaike information criteria, and the generalized Cox-Snell and random quantile residuals. The second one evaluates the size and power of the Wald, likelihood ratio, score, and gradient tests. A web-scraped box-office data set of the movie industry is analyzed to illustrate the proposed approach. Within the main results of the simulation carried out, the good performance of the maximum likelihood estimators is reported.

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Parametric autoregressive moving average models with exogenous terms (ARMAX) have been widely used in the literature. Usually, these models consider a conditional mean or median dynamics, which limits the analysis. In this paper, we introduce a class of quantile ARMAX models based on log-symmetric distributions. This class is indexed by quantile and dispersion parameters. It not only accommodates the possibility to model bimodal and/or light/heavy-tailed distributed data but also accommodates heteroscedasticity. We estimate the model parameters by using the conditional maximum likelihood method. Furthermore, we carry out an extensive Monte Carlo simulation study to evaluate the performance of the proposed models and the estimation method in retrieving the true parameter values. Finally, the proposed class of models and the estimation method are applied to a dataset on the competition "M5 Forecasting -Accuracy" that corresponds to the daily sales history of several Walmart products. The results indicate that the proposed log-symmetric quantile ARMAX models have good performance in terms of model fitting and forecasting.