Análise de séries temporais aplicada às taxas de desemprego no Brasil e em Sergipe no período de 2012 a 2024

Abstract

This paper addresses the study of historical time series of unemployment rates in Brazil and Sergipe from 2012 to 2024, using statistical modeling by the Box and Jenkins method, through the statistical programming language R version 4.4.2. To select the appropriate model, the stationarity of the series was tested by the ADF and KPSS tests, and the AIC criterion was used. For the Brazil series, an ARIMA model (0,2,3)(2,0,0)12 was adjusted, and for the Sergipe series, an ARIMA model (0,1,1). After selecting the model, an analysis of the residuals was performed, in which for the Brazil series, the Ljung Box test presented a p-value of 0.0854, indicating that the series did not present significant correlations in the residuals, and the Shapiro-Wilk test with a p-value of 0.03148, indicating that the adjustment does not follow a normal distribution; for the Sergipe series, the Ljung Box test presented a p-value of 0.766, indicating that there is no significant correlation of the residuals, and the Shapiro-Wilk test presented a pvalue of 0.05609, indicating that the adjustment of the model follows a normal distribution. Finally, the forecasts were made; for the Brazil series, forecasts were made for six and twelve months, and for the Sergipe series, forecasts were made for six quarters.