Previsão da sinistralidade no ramo compreensivo residencial por meio de modelos de séries temporais: uma aplicação às seguradoras Bradesco e Porto Seguro

Abstract

Loss ratio in comprehensive residential insurance is a key indicator for the technical balance of insurance companies, requiring consistent statistical approaches for its analysis and forecasting. This study applies univariate time series models of the SARIMA class to estimate the monthly loss ratio of Bradesco Auto/RE and Porto Seguro, using data from January 2012 to December 2024.Although Itaú Seguros de Auto e Residência S.A. was initially considered due to its relevance in the sector, it was excluded from the forecasting stage as a result of a sharp decline in recent years, which compromised the consistency of its time series.Analyses were conducted in R software, employing graphical tools and statistical tests. The Cox-Stuart test was applied to detect trend, Fisher’s G test for seasonality, and the autocorrelation function and partial autocorrelation function to identify temporal structure. Model selection was based on the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), while predictive accuracy was evaluated using the Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE). The SARIMA(0,1,1)(1,0,0)12 model was fitted to Bradesco with satisfactory performance. For Porto Seguro, the SARIMA(1,0,0)(1,0,2)12 model showed better results, with lower prediction errors and higher adherence to the observed series. The results confirm the applicability of time series modeling as a statistical tool to support actuarial management, contributing to loss ratio control, pricing, and the definition of technical provisions in the insurance sector.