The ModalForecast package implements parametric modal ARIMA models utilizing the Skewed Distribution (SKD) family. Instead of connecting the expected value (mean) to covariates, the model connects the conditional mode to the systematic autoregressive integrated moving average (ARIMA) components.

By modeling the mode directly, this framework helps mitigate the effects of localized extremes, asymmetry, and non-normal behavior, providing robust centralized predictions under asymmetric error distributions.

Methodology

The Skewed Distribution (SKD) Family

To construct a modal regression model, we require a flexible parametric continuous distribution where the mode is explicitly parameterized and differentiable. We adopt the generalized SKD family, which supports robust inference through heavy tails and asymmetry. The package currently implements the Skew-Normal, Skewed Student-t, and Skewed Laplace distributions.

Note on the "normal" distribution: In ModalForecast, specifying dist = "normal" does not invoke the standard symmetric Gaussian distribution. Instead, it refers to the Skew-Normal distribution from the SKD family. The standard normal is recovered asymptotically only when the estimated skewness parameter