Abstract

Time series data constrained to the unit interval arise frequently in environmental and applied sciences and require modeling approaches that respect their bounded support. In this context, a growing body of literature has focused on autoregressive moving average structures combined with non-Gaussian random components, giving rise to the class of unit ARMA-like models. Since the introduction of the beta autoregressive moving average model, numerous extensions have been proposed through the adoption of alternative unit-supported distributions, enabling dynamic modeling of conditional means, medians, or quantiles under serial dependence. This work provides a concise overview of unit ARMA-like model proposals, emphasizing their main methodological developments and underlying distributional assumptions. The practical relevance of this class is illustrated through an application to hourly relative humidity forecasting, using temperature as an exogenous variable and high-frequency data collected from an IoT-enabled weather station installed in a vineyard in Italy. We compare classical ARIMA models with several unit ARMA specifications, including ARMA-like models based on the beta, Kumaraswamy, unit Burr XII, and unit Weibull distributions as random components. Temperature exhibits a significant and predominantly negative effect across all unit ARMA-like formulations. Among the competing models, the unit Weibull ARMA demonstrates superior forecasting performance while preserving theoretical consistency for bounded data. These findings reinforce the suitability of unit ARMA-like models for environmental monitoring applications.
This is a joint work with Anna Vizziello (Department of Electrical, Computer and Biomedical Engineering, University of Pavia; CNIT, Research Unit of the University of Pavia, Italy), Pietro Savazzi (Department of Electrical, Computer and Biomedical Engineering, University of Pavia; CNIT, Research Unit of the University of Pavia, Italy), Emanuele Goldoni (Department of Electrical, Computer and Biomedical Engineering, University of Pavia, Italy), and Paolo Gamba (CNIT, Research Unit of the University of Pavia; University of Pavia, Italy).