Forecasting economic crises is crucial for policymakers and institutions. While various models exist, this paper focuses on the ARIMA model, known for its statistical robustness and application across diverse fields. The study addresses the gap in research concerning quantitative models for predicting economic crises, particularly their impact on healthcare systems. Economic downturns significantly affect health systems, impacting both public (SUS) and private (SSS) sectors in Brazil. Brazil's history of economic crises, including the 2019 unemployment crisis, has underscored the need for effective forecasting tools to manage resource allocation and anticipate shifts in beneficiary patterns between SUS and SSS. The ARIMA model is chosen for its alignment with many linear models, ease of interpretation, and suitability for analyzing time series data. This research contributes to a deeper understanding of crisis dynamics and their effect on Brazil's healthcare sector by applying and evaluating the ARIMA model's performance in predicting five key economic variables.

The introduction extensively reviews existing literature on forecasting models and their applications. It highlights the importance of quantitative models in predicting economic crises and the limited empirical research focusing on the healthcare sector's specific response to such events. The literature emphasizes the need for models that can effectively predict key economic indicators during crises, such as GDP, inflation, and unemployment rates. The review also addresses the interplay between economic downturns and the resilience of healthcare systems, noting the shifts in beneficiary patterns between public and private systems often observed during economic crises. The importance of SDG 3 (health and well-being) within the context of Brazil's economic challenges is also discussed. Previous research on applying ARIMA models to various sectors is cited, highlighting the model's versatility, but pointing out the limited prior research focusing on its use in predicting economic indicators within the Brazilian healthcare context during economic crises.

This study employs an ex-post-facto approach, using secondary data from the IPEA (Institute of Applied Economic Research) and ANS (National Supplementary Health Agency). The ARIMA model is applied to five economic time series: GDP, IPCA, unemployment rate, total health plan beneficiaries, and individual health plan beneficiaries. The methodology involves a two-step process: (i) analyzing the time series to determine the order (p, d, q) of the ARIMA model using autocorrelation and partial autocorrelation functions (ACF and PACF); (ii) selecting the model with the optimal parameters that minimize the sum of squared errors or maximize the likelihood, utilizing criteria like the Akaike Information Criterion (AIC). The maximum likelihood estimation (MLE) method was employed to estimate model parameters. The data spans 2000-2020. The model was first adjusted using data from 2000-2010 and then validated against real data from 2011-2015 using MAPE (Mean Absolute Percentage Error) and U-Theil metrics. After validation, forecasts were generated for the period 2016-2020. The GRETL computational platform was used for ARIMA model implementation. The paper explains the ARIMA model's mathematical foundation, including the concepts of autoregressive (AR), integrated (I), and moving average (MA) components, the process of differencing to achieve stationarity, and the interpretation of ACF and PACF plots in selecting the appropriate model order. Equations are provided to show the mathematical representation of the ARIMA model and the calculation of error metrics.

The ARIMA model demonstrated high accuracy in forecasting all five economic time series. Specific ARIMA models were identified for each variable: ARIMA (1,0,2) for GDP, ARIMA (2,2,1) for IPCA, ARIMA (0,1,2) for the unemployment rate, ARIMA (1,1,2) for total health plan beneficiaries, and ARIMA (2,2,1) for individual health plan beneficiaries. The MAPE and U-Theil values were used to assess model performance. For example, the MAPE for GDP forecasting was 9.16%, and the U-Theil was 0.617. Similar results demonstrating high predictive accuracy with MAPE values consistently under 15% and U-Theil values below 0.62 are reported for the other variables. The models consistently achieved over 95% prediction accuracy, as evidenced by the figures presented in the paper, providing visual representation of the model's fit to the data. The study’s findings reveal significant variations in economic indicators (GDP and IPCA) and health plan beneficiaries throughout the years. Tables and figures depict the forecasts for 2016-2020 and the corresponding percentage variations for each variable. A detailed descriptive analysis of the datasets for each variable is provided, including mean, standard deviation, min, max, skew, and kurtosis, offering a deeper understanding of data distribution and variability.

The study's findings confirm the ARIMA model's effectiveness in forecasting key economic variables relevant to Brazil's healthcare sector during economic crises. The high accuracy of the predictions demonstrates the model's potential for informing strategic decision-making in resource allocation, preparedness for shifts in public health demand, and adjustments to service provision. The results highlight the importance of considering economic downturns and the interplay between public and private healthcare systems. The ability to forecast the unemployment rate and the number of health plan beneficiaries (both total and individual) is particularly valuable for planning and resource management in both the SUS and SSS. The paper discusses the implications of the findings for the sustainability of health plan operators (OPSs) and the challenges faced by the Brazilian private healthcare sector. The study's findings are discussed in relation to the literature on forecasting models, and the strengths and limitations of the ARIMA model are acknowledged. The results are contextualized within the Brazilian economic landscape and its complex healthcare system.

The research demonstrates ARIMA's capacity to accurately predict essential economic variables impacting Brazil's healthcare system, exceeding 95% accuracy. This facilitates strategic planning, especially during economic downturns. Future research should explore non-linear models, including AI and fuzzy logic, and analyze the impact of events like the COVID-19 pandemic. Further empirical research on ARIMA and other models for specific healthcare sector challenges is also recommended. The study's findings emphasize the model’s versatility, while noting the need to acknowledge limitations for abrupt data shifts and long-term prediction.

The study acknowledges limitations inherent in using historical data patterns to predict future events, especially during economic crises. The ARIMA model's linear nature may not fully capture non-linear relationships or external influences on the time series. The authors note that the model's parameter estimations have inherent uncertainty, and the assumption of persistent historical patterns may not always hold true, especially during periods of significant economic upheaval. The study’s focus is on Brazil, limiting the generalizability of the findings to other contexts. While the model demonstrates high accuracy, the study suggests exploring additional sophisticated methods for even greater accuracy.