Abstract

The unit Rayleigh (UR) distribution is a one-parameter model suitable for modeling skewness unimodal data. In this study, we consider a quantile re-parametrization for the UR distribution and propose an autoregressive moving average (ARMA) structure based on it. We aim to provide a simple alternative for modeling double-bounded variables under serial correlation in a conditional quantile of the UR distribution. Given that the parent model represents a one-parameter distribution, our introduced model is more parsimonious than the commonly used for ARMA time series. We discuss a conditional maximum likelihood approach for estimating the model parameters and present a Monte Carlo simulation study to evaluate its performance in finite samples. A notable feature of this approach is its simplicity. The parsimony of the model and its straightforward quantile function add significant appeal to this novel proposal when compared to other unit distribution such as the beta, Kumaraswamy, and unit Weibull models. As future work, we aim to illustrate the usefulness of the proposed methodology through applications to real datasets. The proposed model has the potential to enhance the understanding of stochastic behavior and the quality of forecasts for various double-bounded indicators, including those defined for monitoring hydro-environmental problems, many of which are expressed as rates and proportions. Additionally, the UR distribution under the ARMA structure represents an innovative approach with applicability extendable to several areas dealing with the necessity of forecasting double-bounded indicators.