  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.
