This paper discusses dynamic ARMA-type regression models for positive time series, which can handle bounded non-Gaussian time series without requiring data transformations. Our proposed model includes a conditional mean modeled by a dynamic structure containing autoregressive and moving average terms, time-varying covariates, unknown parameters, and link functions. Additionally, we present the PTSR package and discuss partial maximum likelihood estimation, asymptotic theory, hypothesis testing inference, diagnostic analysis, and forecasting for a variety of regression-based dynamic models for positive time series. A Monte Carlo simulation and a real data application are provided.

Oil has become a prevalent global pollutant, stimulating the research to improve the techniques to separate oil from water. Materials with special wetting properties—primarily those that repel water while attracting oil—have been proposed as suitable candidates for this task. However, one limitation in developing efficient substrates is the limited available volume for oil absorption. In this study, we investigate the efficacy of disordered fractal materials in addressing this challenge, leveraging their unique wetting properties. Using a combination of a continuous model and Monte Carlo simulations, we characterize the hydrophobicity and oleophilicity of substrates created through ballistic deposition (BD). Our results demonstrate that these materials exhibit high contact angles for water, confirming their hydrophobic nature while allowing significant oil penetration, indicative of oleophilic behavior. The available free volume within the substrates varies from 60% to 90% of the total volume of the substrate depending on some parameters of the BD. By combining their water and oil wetting properties with a high availability of volume, the fractal substrates analyzed in this work achieve an efficiency in separating oil from water of nearly 98%, which is significantly higher compared to micro-pillared surfaces made from the same material but lacking a fractal design.