COMPARISON OF ARIMA AND GARMA'S PERFORMANCE ON DATA ON POSITIVE COVID-19 CASES IN INDONESIA

Keywords: ARIMA, GARMA, AIC, Covid-19, Indonesia

Abstract

The development of methods in statistics, one of which is used for prediction, is overgrowing. So it requires further analysis related to the goodness of the method. One of the comparisons made to the goodness of this model can be seen by applying it to actual cases around us. The real case still being faced by people worldwide, including in Indonesia, is Covid-19. Therefore, research comparing the autoregressive integrated moving average (ARIMA) and the Gegenbauer autoregressive moving average (GARMA) method in positive confirmed cases of Covid-19 in Indonesia is essential. Based on the results of this research analysis, it was found that the best model with the Aikake's Information Criterion measure of goodness that was used to predict positive confirmed cases of Covid-19 in Indonesia was the Gegenbauer autoregressive moving average (GARMA) model.

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Author Biographies

A'yunin Sofro, Universitas Negeri Surabaya

Department of Mathematics

Khusnia Nurul Khikmah, IPB University

Department of Statistics

References

M. A. Hernán, J. Hsu, and B. Healy, “A second chance to get causal inference right: a classification of data science tasks,” Chance, vol. 32, no. 1, pp. 42–49, 2019.

T. Chakraborty and I. Ghosh, “Real-time forecasts and risk assessment of novel coronavirus (COVID-19) cases: A data-driven analysis,” Chaos, Solitons & Fractals, vol. 135, p. 109850, 2020.

A. Hernandez-Matamoros, H. Fujita, T. Hayashi, and H. Perez-Meana, “Forecasting of COVID19 per regions using ARIMA models and polynomial functions,” Appl. Soft Comput., vol. 96, p. 106610, 2020.

G. S. Dissanayake, M. S. Peiris, and T. Proietti, “Fractionally differenced Gegenbauer processes with long memory: A review,” Stat. Sci., vol. 33, no. 3, pp. 413–426, 2018.

E. Beard et al., “Understanding and using time series analyses in addiction research,” Addiction, vol. 114, no. 10, pp. 1866–1884, 2019.

M. Fernandes, A. Canito, J. M. Corchado, and G. Marreiros, “Fault detection mechanism of a predictive maintenance system based on autoregressive integrated moving average models,” in International Symposium on Distributed Computing and Artificial Intelligence, 2019, pp. 171–180.

H. Yan, G. W. Peters, and J. Chan, “Mortality models incorporating long memory for life table estimation: a comprehensive analysis,” Ann. Actuar. Sci., vol. 15, no. 3, pp. 567–604, 2021.

S. Ben Amor, H. Boubaker, and L. Belkacem, “Forecasting electricity spot price for Nord Pool market with a hybrid k‐factor GARMA–LLWNN model,” J. Forecast., vol. 37, no. 8, pp. 832–851, 2018.

F. Maddanu and T. Proietti, “Modelling Persistent Cycles in Solar Activity,” Sol. Phys., vol. 297, no. 1, pp. 1–22, 2022.

H. Yan, G. W. Peters, and J. S. K. Chan, “Multivariate long-memory cohort mortality models,” ASTIN Bull. J. IAA, vol. 50, no. 1, pp. 223–263, 2020.

Y. Cao, Q. Deng, and S. Dai, “Remdesivir for severe acute respiratory syndrome coronavirus 2 causing COVID-19: An evaluation of the evidence,” Travel Med. Infect. Dis., vol. 35, p. 101647, 2020.

J. Fattah, L. Ezzine, Z. Aman, H. El Moussami, and A. Lachhab, “Forecasting of demand using ARIMA model,” Int. J. Eng. Bus. Manag., vol. 10, p. 1847979018808673, 2018.

M. B. Shrestha and G. R. Bhatta, “Selecting appropriate methodological framework for time series data analysis,” J. Financ. Data Sci., vol. 4, no. 2, pp. 71–89, 2018.

K. E. ArunKumar, D. V Kalaga, C. M. S. Kumar, G. Chilkoor, M. Kawaji, and T. M. Brenza, “Forecasting the dynamics of cumulative COVID-19 cases (confirmed, recovered and deaths) for top-16 countries using statistical machine learning models: Auto-Regressive Integrated Moving Average (ARIMA) and Seasonal Auto-Regressive Integrated Moving Averag,” Appl. Soft Comput., vol. 103, p. 107161, 2021.

C. W. J. Granger and R. Joyeux, “An introduction to long‐memory time series models and fractional differencing,” J. time Ser. Anal., vol. 1, no. 1, pp. 15–29, 1980.

A. K. Diongue and M. Ndongo, “The k-factor GARMA process with infinite variance innovations,” Commun. Stat. Comput., vol. 45, no. 2, pp. 420–437, 2016.

P. Beaumont and A. Smallwood, “Conditional Sum of Squares Estimation of Multiple Frequency Long Memory Models,” 2019.

J. E. Cavanaugh and A. A. Neath, “The Akaike information criterion: Background, derivation, properties, application, interpretation, and refinements,” Wiley Interdiscip. Rev. Comput. Stat., vol. 11, no. 3, p. e1460, 2019.

W. Wang and Y. Lu, “Analysis of the mean absolute error (MAE) and the root mean square error (RMSE) in assessing rounding model,” in IOP conference series: materials science and engineering, 2018, vol. 324, no. 1, p. 12049.

S. Theocharides, G. Makrides, A. Livera, M. Theristis, P. Kaimakis, and G. E. Georghiou, “Day-ahead photovoltaic power production forecasting methodology based on machine learning and statistical post-processing,” Appl. Energy, vol. 268, p. 115023, 2020.

Published
2022-09-01
How to Cite
[1]
A. Sofro and K. Khikmah, “COMPARISON OF ARIMA AND GARMA’S PERFORMANCE ON DATA ON POSITIVE COVID-19 CASES IN INDONESIA”, BAREKENG: J. Math. & App., vol. 16, no. 3, pp. 919-926, Sep. 2022.