O modelo unit-Lindley autorregressivo e de médias móveis (ULARMA) aplicado no monitoramento e previsão de dados contínuos no intervalo unitário.

Abstract

In this work, we propose statistical models for the analysis of data that exhibit variation over time. In particular, when the variable (or characteristic) of interest is continuous in the interval (0,1), as is the case with rates, proportions, and indices. The unit-Lindley distribution stands out among the probability distributions in the unit interval that have been introduced in recent literature and have interesting and useful properties (e.g., a single parameter, reparameterized version in terms of the mean, closed expressions for moments). In this work, the unit-Lindley autoregressive and moving average (ULARMA) model is proposed, as an extension of the unit-Lindley distribution for the case of autocorrelated data. Furthermore, to take control of future observations of the process, control charts are also presented for monitoring and forecasting data of this type. Numerical simulation studies are carried out to evaluate the performance of estimation procedures (e.g., based on the conditional maximum likelihood method) and control charts (e.g., based on the proposed time series model with a continuous response variable in (0,1) described by the unit-Lindley distribution). Finally, the methodology developed here is illustrated in a set of real data with information on maximum and minimum values of daily relative air humidity in the Atacama Desert, located in the north of Chile, in order to verify its applicability in a practical context, when compared to traditional/existing techniques.