GLARMA Model for Temporal Data Analysis: extensions for positive continuous data and a bootstrap proposal for inference on model parameters

Abstract

With the frequent occurrence in our daily lives of phenomena related to meteorological variables such as precipitation and temperature, atmospheric pollutant concentration, and financial variables, it becomes essential to develop flexible models for the adequate treatment of this data. With this purpose, an extension of the Generalized Linear Autoregressive Moving Average (GLARMA) model has been developed to encompass positive continuous responses, thereby expanding the applicability of the model. Previously restricted to count data, the model is now capable of handling a wider variety of data types, providing a more versatile and effective tool for analysis and prediction across various fields of study. Furthermore, this work also focuses on the construction of procedures for inference on the parameters of the GLARMA model without making assumptions about the shape of the data distribution. To achieve this, we introduced the conditional parametric bootstrap procedure in the construction of confidence intervals and hypothesis testing for the parameters of the GLARMA model. Additionally, through this procedure, we were able to correct biases in estimators when the sample size is small. Numerical studies are conducted to evaluate the performance of the proposed extension and the bootstrap procedure in different scenarios. Demonstrating the utility of the proposals in real situations, three analyses of real data are performed considering atmospheric, epidemiological, and financial variables.