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Short-term forecasting COVID-19 cumulative confirmed cases: Perspectives for Brazil
Matheus Henrique Dal Molin Ribeiro, Ramon Gomes da Silva, Viviana Cocco Mariani, Leandro dos Santos Coelho
TL;DR
The paper addresses short-term forecasting of COVID-19 cumulative confirmed cases to support public-health planning in Brazil. It compares statistical, machine-learning, and stacking models across ten states and one-, three-, and six-day horizons, finding SVR and stacking generally most suitable, while recommending cautious use because of chaotic data dynamics.
Problem
Accurate epidemiological forecasting is needed to support strategic public-health planning during the COVID-19 pandemic.
Method
The study compares ARIMA, CUBIST, RF, RIDGE, SVR, and stacking-ensemble models for one-, three-, and six-days-ahead forecasting across ten Brazilian states.
Results
SVR and stacking-ensemble learning are suitable for most states, with the overall model ranking SVR, stacking ensemble, ARIMA, CUBIST, RIDGE, and RF.
Takeaways & Limitations
The evaluated models can assist managers in forecasting and monitoring COVID-19 case growth for decision-support systems.
Takeaways & Limitations
The study’s future work proposes deep-learning stacking, data augmentation for small samples, hyperparameter optimization, and features to explain future cases.
Abstract
from arXiv · showhide
The new Coronavirus (COVID-19) is an emerging disease responsible for infecting millions of people since the first notification until nowadays. Developing efficient short-term forecasting models allow knowing the number of future cases. In this context, it is possible to develop strategic planning in the public health system to avoid deaths. In this paper, autoregressive integrated moving average (ARIMA), cubist (CUBIST), random forest (RF), ridge regression (RIDGE), support vector regression (SVR), and stacking-ensemble learning are evaluated in the task of time series forecasting with one, three, and six-days ahead the COVID-19 cumulative confirmed cases in ten Brazilian states with a high daily incidence. In the stacking learning approach, the cubist, RF, RIDGE, and SVR models are adopted as base-learners and Gaussian process (GP) as meta-learner. The models' effectiveness is evaluated based on the improvement index, mean absolute error, and symmetric mean absolute percentage error criteria. In most of the cases, the SVR and stacking ensemble learning reach a better performance regarding adopted criteria than compared models. In general, the developed models can generate accurate forecasting, achieving errors in a range of 0.87% - 3.51%, 1.02% - 5.63%, and 0.95% - 6.90% in one, three, and six-days-ahead, respectively. The ranking of models in all scenarios is SVR, stacking ensemble learning, ARIMA, CUBIST, RIDGE, and RF models. The use of evaluated models is recommended to forecasting and monitor the ongoing growth of COVID-19 cases, once these models can assist the managers in the decision-making support systems.
1. Introduction
The paper addresses COVID-19’s public-health impacts by comparing statistical and machine-learning models for short-term forecasting of cumulative cases in Brazil. It evaluates heterogeneous models, stacking, and multiple forecast horizons to support pandemic planning and decision-making.
- Motivation: COVID-19 created urgent concerns about outbreak peaks, duration, and eventual infections, alongside substantial effects on lives and the economy.
- Motivation: Accurate epidemiological forecasting can support strategic planning in public-health systems and help managers avoid possible epidemics.
- Study objective: The study compares ARIMA, CUBIST, RF, RIDGE, SVR, and stacking models for one-, three-, and six-days-ahead cumulative-case forecasts in ten Brazilian states.The stacking model uses CUBIST, RF, RIDGE, and SVR as base-learners and Gaussian process as meta-learner.
- Study objective: The research evaluates forecasting efficiency using improvement percentage index, mean absolute error, and symmetric mean absolute percentage error.
- Contributions: The contributions include a novel analysis of Brazilian cumulative confirmed-case forecasting intended to assist governors with pandemic containment and health-system strategies.
- Contributions: The paper introduces heterogeneous machine-learning models and stacking-ensemble learning for forecasting Brazilian cumulative confirmed cases.
- Contributions: Evaluating one-, three-, and six-days-ahead horizons allows model effectiveness to be examined across different scenarios for future COVID-19 strategies.
2. Material and Methods
The study analyzes cumulative COVID-19 cases from ten Brazilian states and compares statistical, machine-learning, and stacking models for forecasting. The selected models include ARIMA, CUBIST, GP, RIDGE, RF, SVR, and stacking.
- Dataset Description: The dataset contains cumulative confirmed COVID-19 cases from ten Brazilian states, collected through April 18 or 19, 2020.The states include Amazonas, Bahia, Ceara, Minas Gerais, Parana, Rio de Janeiro, Rio Grande do Norte, Rio Grande do Sul, Santa Catarina, and Sao Paulo.
- Dataset Description: The measurement period varies by state, running from its first reported case through its last report.The paper notes that health-department accounting changes may alter the presented data.
- Forecasting Models: ARIMA models non-stationary time series using autoregressive, differencing, and moving-average components.Its order is represented as ARIMA(p,d,q) and may be selected through grid-search and autocorrelation analyses.
- Forecasting Models: CUBIST uses rule-based regression trees and neighborhood information, while RF combines bootstrap samples with randomly selected predictors in decision trees.These models represent distinct tree-based approaches used in the comparison.
- Forecasting Models: RIDGE applies penalization to ordinary least squares, helping control parameter-estimate variability and address input multicollinearity.SVR uses kernel functions and is described as capable of capturing predictor non-linearity.
- Forecasting Models: Stacking combines predictions from CUBIST, RF, RIDGE, and SVR through a Gaussian-process meta-learner.The paper describes stacking as a two-level ensemble approach intended to improve accuracy and reduce error variance.
3. Proposed forecasting framework
The forecasting framework splits the data into training and test sets, fits models using past case observations, and recursively generates forecasts up to six days ahead. Out-of-sample predictions are evaluated with improvement index, MAE, and sMAPE.
- Data Preparation: The test set contains the six latest observations, while the remaining observations form the training set.Training data are centered by their mean and scaled by their standard deviation.
- Recursive Forecasting: The framework uses a recursive strategy in which forecasts become inputs for subsequent multi-day predictions.This extends a one-day-ahead model to longer forecasting horizons.
- Recursive Forecasting: The forecasting function uses five past confirmed-case observations, with the lag value selected through grid-search.The selected lag is intended to capture the best data behavior.
- Forecasting Horizons: The framework targets one-, three-, and six-days-ahead forecasts, labeled ODA, TDA, and SDA, respectively.These horizons support evaluation across multiple forecasting scenarios.
- Stacking and Evaluation: Stacking trains CUBIST, RF, RIDGE, and SVR as base-learners whose forecasts become inputs to a GP meta-learner.Time-slice leave-one-out cross-validation is used during training, followed by out-of-sample forecasting.
- Stacking and Evaluation: Model effectiveness is assessed on out-of-sample forecasts using IP, MAE, and sMAPE criteria.The evaluation compares observed and predicted values, with Mc and Mb denoting compared and best models in the performance measure.
4. Results
Across 180 forecasting scenarios, model performance varied by state and horizon, with SVR, stacking, and ARIMA often strongest. Best-state sMAPE ranged from 0.87%–3.51% one day ahead to 0.95%–6.90% six days ahead.
- SVR outperformed other models across all forecasting windows in BA, MG, RS, and SP for MAE and sMAPE.
- ARIMA performed best for CE at ODA and TDA, while SVR performed best at SDA; in RN, CUBIST performed best at SDA.
- Stacking ensemble was generally best for PR, RJ, and SC, except that ARIMA performed better at ODA.
- 180 scenarios combined ten datasets, three forecasting horizons, and six models for cumulative COVID-19 case forecasting.
- Best-state sMAPE ranged from 0.87%–3.51% for ODA, 1.02%–5.63% for TDA, and 0.95%–6.90% for SDA.
- Overall model ranking was SVR, stacking ensemble, ARIMA, CUBIST, RIDGE, and RF; ARIMA weakened at SDA, while RF required more observations.
- Box-plots showed that smaller error variation indicated greater stability, and lower-error models achieved more homogeneous prediction errors.
5. Conclusion and Future Research
The study evaluates six approaches for short-term COVID-19 case forecasting across ten Brazilian states and three horizons. SVR and stacking were suitable for most states, but forecasts should be used cautiously because chaotic dynamics and exogenous factors affect notifications.
- Six models forecast one-, three-, and six-days-ahead cumulative COVID-19 cases across ten Brazilian states using IP, MAE, and sMAPE criteria.
- SVR and stacking-ensemble learning were suitable for forecasting cases in most adopted states because they learned nonlinearities in the epidemiological time series.
- The models should be used cautiously because analyzed data have chaotic dynamics and daily notifications are affected by diverse exogenous factors.
- Future work includes combining deep learning with stacking, using copulas for small-sample augmentation, optimizing hyperparameters, and adding explanatory features.
CRediT Author Statement
The author statement assigns conceptualization, methodology, formal analysis, validation, and writing roles across the contributors.
- Matheus Henrique Dal Molin Ribeiro and Ramon Gomes da Silva contributed to conceptualization, methodology, formal analysis, validation, and writing.
- Viviana Cocco Mariani and Leandro dos Santos Coelho contributed to conceptualization and writing review and editing.
Appendix A. Performance Measures
Appendix A presents performance measures for each evaluated model across states and forecasting horizons.
- Table A.1 reports performance measures for each model in each state and forecasting horizon.
Appendix B. Hyperparameters
Appendix B presents the hyperparameters selected for each evaluated model through grid-search.
- Table B.1 lists hyperparameters selected by grid-search for each evaluated model.The stacking model's GP meta-learner has no hyperparameter to tune.