Modelagem de séries temporais para previsão da quantidade de micro e pequenas empresas atendidas pelo Sebrae/RN

Abstract

This study investigates the application of time series analysis to monthly data on the number of Individual Microentrepreneurs (MEI), Microenterprises (ME), and Small Businesses (EPP) served by Sebrae/RN from January 2014 to December 2023, aiming to forecast the future number of distinct attendances for these business categories. The main objective is to fit a dynamic regression model with SARIMA errors (SARIMAE), using the number of attendances performed by Sebrae as the regressor variable. The study selects the most appropriate model for each category of interest, makes forecasts for 24 steps ahead, and compares the forecasts for the first 12 steps with the observed data, using the root mean squared error (RMSE) as the evaluation criterion, in addition to making forecasts for the year 2024 for the last 12 steps. For the analysis, the dataset was divided into training and testing sets, covering the period from January 2014 to December 2022 for training and the year 2023 for testing. The modeling process included model identification, parameter evaluation, diagnostic of the selected models, and forecasting. The results indicate a gradual increase in the number of distinct attendances over time, with a significant increase observed in 2023 for all studied variables. Among the analyzed models, SARIMAE(2,1,1)(0,1,3) proved to be the most suitable for forecasting the number of MEIs served with the number of MEI attendances as the regressor variable, SARIMAE(3,1,1)(0,1,1) for the number of MEs served with the number of ME attendances as the regressor variable, and SARIMA(0,0,2)(0,1,1) for the number of EPPs served.