COMPARATIVE PERFORMANCE ANALYSIS OF ARIMA, PROPHET AND HOLT-WINTERS FORECASTING METHODS ON EUROPEAN COVID-19 DATA

Nur Şebnem Ersöz; Pınar Güner; Ayhan Akbaş; Burcu Bakir-gungor

doi:10.46519/ij3dptdi.1120718

Research Article

COMPARATIVE PERFORMANCE ANALYSIS OF ARIMA, PROPHET AND HOLT-WINTERS FORECASTING METHODS ON EUROPEAN COVID-19 DATA

Year 2022, Volume: 6 Issue: 3, 556 - 565, 31.12.2022

Nur Şebnem Ersöz , Pınar Güner , Ayhan Akbaş , Burcu Bakir-gungor

https://doi.org/10.46519/ij3dptdi.1120718

Cited By: 4

Abstract

COVID-19 son yılların en bulaşıcı hastalığıdır ve dünyanın her yerinde salgına neden olmuştur. Daha önce yüzlerce olan ölüm oranı önce binlere, sonra milyonlara yükselmiştir. Ocak 2020'den beri birçok bilim insanı, hükümetlerin hastanelerde yeterli düzenlemeleri yapabilmesi ve ölüm oranını azaltılabilmesi için COVID-19’un yayılımını anlamaya ve tahminlemeye çalışıyor. Bu araştırma makalesi, Avrupa’daki COVID-19 hastalık epidemiyolojisi için tahminler yapmak amacıyla, ARIMA, Prophet ve Holt Winters Üstel Düzeltme yöntemlerinin performans karşılaştırmasını sunmaktadır. Veri seti olarak, Dünya Sağlık Örgütü (DSÖ)'nün toplayıp kategorize ettiği, Avrupa ülkelerinin 2020 ile 2022 yılları arasındaki COVID-19 vaka verileri kullanılmıştır. Elde edilen sonuçlar, Holt-Winters Üstel Düzeltme (RMSE: 0.20, MAE: 0.17) yönteminin, ARIMA ve Prophet tahmin yöntemlerinden daha iyi performans gösterdiğini belirtmektedir.

Keywords

COVID-19,, Zaman Serisi Tahmini,, ARIMA,, Prophet,, Holt Winters Üstel Düzeltme

References

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3. Reuters Covid-19 Tracker “Europe: the latest coronavirus counts, charts and maps,” Reuters. https://graphics.reuters.com/world-coronavirus-tracker-and-maps/regions/europe/ September 05, 2022.
4. Sevinç, E., “An empowered AdaBoost algorithm implementation: A COVID-19 dataset study,” Comput. Ind. Eng., Vol. 165, 107912, 2022
5. Deniz A., Kiziloz, H.E., Sevinc, E., and Dokeroglu, T., “Predicting the severity of COVID-19 patients using a multi-threaded evolutionary feature selection algorithm,” Expert Syst., Vol. 39, Issue. 5, 12949, 2022
6. Karahan, M., “Yapay Sinir Ağları Metodu İle İhracat Miktarlarının Tahmini: ARIMA ve YSA Metodunun Karşılaştırmalı Analizi,” Ege Akad. Bakis Ege Acad. Rev., Vol. 15, Issue 2, Pages 165–165, Apr. 2015
7. Almasarweh, M., “ARIMA Model in Predicting Banking Stock Market Data,” Mod. Appl. Sci., Vol. 12, Issue. 11, p. 4, 2018.
8. Karahan., M., “Forecasting Amount of Export Demand with Artificial Neural Networks Method: A Comparative Analysis of ARIMA and ANN,” Ege Academic Review, Vol. 15, Issue 2, Pages 165–172, 2015.
9. Li, Z., Li, Y., “A comparative study on the prediction of the BP artificial neural network model and the ARIMA model in the incidence of AIDS,” BMC Med. Inform. Decis. Mak., Vol. 20, Issue 1, 2020 .
10. Wang, Y. W., Shen, Z. Z., Jiang, Y., “Comparison of ARIMA and GM(1,1) models for prediction of hepatitis B in China,” PloS One, Vol. 13, Issue 9, 2018.
11. Earnest, A., Evans, S.M., Sampurno, F., Millar, J., “Forecasting annual incidence and mortality rate for prostate cancer in Australia until 2022 using autoregressive integrated moving average (ARIMA) models,” BMJ Open, Vol. 9, Issue. 8, 2019
12. Yang, J., Li, L., Shi, Y., Xie, X., “An ARIMA Model With Adaptive Orders for Predicting Blood Glucose Concentrations and Hypoglycemia,” IEEE J. Biomed. Health Inform., Vol. 23, Issue. 3, Pages 1251–1260, 2019.
13. Zheng, A., Fang, Q., Zhu, Y., Jiang, C., Jin, F., Wang, X., “An application of ARIMA model for predicting total health expenditure in China from 1978-2022,” J. Glob. Health, Vol. 10, Issue. 1, 2020.
14. Li, Z., Wang, Z., Song, H., Liu, Q., He, B., Shi, P., Ji, Y., Xu, D., Wang, J., “Application of a hybrid model in predicting the incidence of tuberculosis in a Chinese population,” Infect. Drug Resist., Vol. 12, Pages 1011–1020, 2019.
15. Wang, L., Liang, C., Wu, W., Wu, S., Yang, J., Lu, X., Cai, Y., Jin, C.,, “Epidemic Situation of Brucellosis in Jinzhou City of China and Prediction Using the ARIMA Model,” Can. J. Infect. Dis. Med. Microbiol., Vol. 2019, 2019.
16. Zhai, M., Li, W., Tie, P., Wang, X., Xie, T., Ren, H., Zhang, Z., Song, W., Quan, D., Li, M., Chen, L., Qui, L., “Research on the predictive effect of a combined model of ARIMA and neural networks on human brucellosis in Shanxi Province, China: a time series predictive analysis,” BMC Infect. Dis., Vol. 21, Issue. 1, p. 280, 2021.
17. Adeyinka, D.A., Muhajarine, N., “Time series prediction of under-five mortality rates for Nigeria: comparative analysis of artificial neural networks, Holt-Winters exponential smoothing and autoregressive integrated moving average models,” BMC Med. Res. Methodol., Vol. 20, Issue 1, 2020.
18. Ryu, S., Nam, H. J., Kim, J. M., Kim, S. W., “Current and Future Trends in Hospital Utilization of Patients With Schizophrenia in Korea: A Time Series Analysis Using National Health Insurance Data,” Psychiatry Investig., Vol. 18, Issue. 8, Pages 795–800, 2021.
19. Ceylan, Z., “Estimation of COVID-19 prevalence in Italy, Spain, and France,” Sci. Total Environ., Vol. 729, 2020.
20. Fang, L., Wang, D., Pan, G., “Analysis and Estimation of COVID-19 Spreading in Russia Based on ARIMA Model,” SN Compr. Clin. Med., Vol. 2, Issue 12, Pages 2521–2527, 2020.
21. Swaraj, A., Verma, K., Kaur, A., Singh, G., Kumar, A., de Sales, L. M., “Implementation of stacking based ARIMA model for prediction of Covid-19 cases in India,” J. Biomed. Inform., Vol. 121, 2021.
22. Dinmohamed, A. G., Cellamare, M., Visser, O., de Munck, L., Elferink, M. A., Westenend, P. J., Wesseling, J., Broeders, M. J. M., Kuipers, E. J., Merkx, A. W., Nagtegaal, I. D., Siesling, S., , “The impact of the temporary suspension of national cancer screening programmes due to the COVID-19 epidemic on the diagnosis of breast and colorectal cancer in the Netherlands,” J. Hematol. Oncol.J Hematol Oncol, Vol. 13, Issue 1, 2020.
23. Dash, S., Chakraborty, C., Giri, S. K. Pani, S. K., “Intelligent computing on time-series data analysis and prediction of COVID-19 pandemics,” Pattern Recognit. Lett., Vol. 151, Pages 69–75, 2021.
24. Tulshyan, V., Sharma, D., Mittal, M., “An Eye on the Future of COVID-19: Prediction of Likely Positive Cases and Fatality in India over a 30-Day Horizon Using the Prophet Model,” Disaster Med. Public Health Prep., Pages 1–7, 2020.
25. Aydin, A., “Analysis of the effects of the Covid-19 epidemic on the Turkish air transport sector with the ARIMA model.” Ardahan Universitesi IIBF Dergisi Vol 3, Issue 2, Pages 118-127, 2021.
26. Battineni, G., Chintalapudi, N., Amenta, F., “Forecasting of COVID-19 epidemic size in four high hitting nations (USA, Brazil, India and Russia) by Fb-Prophet machine learning model,” Appl. Comput. Inform., 2020.
27. Kopanitsa, G., Metsker, O., Yakovlev, A., Fedorenko, A., Zvartau, N., “Modelling of COVID-19 Morbidity in Russia,” Stud. Health Technol. Inform., Vol. 273, Pages 262–265, 2020.
28. Talkhi, N., Fatemi, N. A., Ataei, Z., Nooghabi, M. J., “Modeling and forecasting number of confirmed and death caused COVID-19 in IRAN: A comparison of time series forecasting methods,” Biomed. Signal Process. Control, Vol. 66, 2021.
29. Djakaria I., Saleh, S. E., “Covid-19 forecast using Holt-Winters exponential smoothing,” J. Phys. Conf. Ser., Vol. 1882, Issue. 1, 2021.
30. World Health Organisation “WHO Coronavirus (COVID-19)Dashboard.” https://covid19.who.int April 28, 2022.
31. Alabdulrazzaq, H., Alenezi, M. N., Rawajfih, Y., Alghannam, B. A., Al-Hassan, A. A., Al-Anzi, F. S., “On the accuracy of ARIMA based prediction of COVID-19 spread” Results in Pyhsics, Vol. 27, 2021.
32. Taylor, S. J., Letham, B., “Forecasting at Scale,” Am. Stat., Vol. 72, Issue. 1, Pages 37–45, 2018.
33. Mahanty, M., Swathi, K. Teja, K. S., Bhattacharyya, D., “A Prophet Model to Forecast Spread of Covid-19 Pandemic,” Journal of Xidian University, Vol 14, Issue 7, Pages 949-962, 2020.
34. Panda, M., “Application of ARIMA and Holt-Winters forecasting model to predict the spreading of COVID-19 for India and its states,” medRxiv, 2020.
35. Kalekar, P. S., “Time series Forecasting using Holt-Winters Exponential Smoothing,” Time Ser. Forecast. Using Holt-Winters Exponential Smoothing” Environmental Science Jan. 2004.
36. Koehler, A. B., Snyder, R. D., Ord, J. K., “Forecasting models and prediction intervals for the multiplicative Holt-Winters method,” Int. J. Forecast., Vol. 17, Pages 269–286, 2001.
37. Satrio, C. B. A., Darmawan, W., Nadia, B. U., Hanafiah, N., “Time series analysis and forecasting of coronavirus disease in Indonesia using ARIMA model and PROPHET,” Procedia Comput. Sci., Vol. 179, Pages 524–532, 2021
38. Bögl, M., Aigner, W., Filzmoser, P., Lammarsch, T., Miksch, S., Rind, A., “Visual Analytics for Model Selection in Time Series Analysis,” IEEE Trans. Vis. Comput. Graph., Vol. 19, Issue. 12, Pages 2237–2246, 2013.
39. Akay, S., Akay, H., "Time series model for forecasting the number of COVID-19 cases in Turkey", Turkish Journal of Public Health, Vol. 19, Issue. 2, Pages 140-145, 2021.
40. Abdussalam, W., Mertel, A., Fan, K., Schüler, L., Schlechte-Wełnicz, W., Calabrese, J. M., “A scalable pipeline for COVID-19: the case study of Germany, Czechia and Poland.” arXiv, 2022.

COMPARATIVE PERFORMANCE ANALYSIS OF ARIMA, PROPHET AND HOLT-WINTERS FORECASTING METHODS ON EUROPEAN COVID-19 DATA

Year 2022, Volume: 6 Issue: 3, 556 - 565, 31.12.2022

Nur Şebnem Ersöz , Pınar Güner , Ayhan Akbaş , Burcu Bakir-gungor

https://doi.org/10.46519/ij3dptdi.1120718

Cited By: 4

Abstract

COVID-19 is the most common infectious disease of the last few years and has caused an outbreak all around the world. The mortality rate, which was earlier in the hundreds, increased to thousands and then to millions. Since January 2020, several scientists attempted to understand and predict the spread of COVID-19 so that governments may make sufficient arrangements in hospitals and reduce the mortality rate. This research article presents a comparative performance analysis of ARIMA, Prophet and Holt-Winters Exponential Smoothing forecasting methods to make predictions for the COVID-19 disease epidemiology in Europe. The dataset has been collected from the World Health Organization (WHO) and includes the COVID-19 case data of European countries, which is categorized by WHO between the years of 2020 and 2022. The results indicate that Holt-Winters Exponential Smoothing method (RMSE: 0.2080, MAE: 0.1747) outperforms ARIMA and Prophet forecasting methods.

Keywords

COVID-19, Time Series Forecasting, ARIMA, Prophet, Holt-Winters Exponential Smoothing

References

1. Chams, N., Chams, S., Badran, R., Shams, A., Araji, A., Raad, M Mukhopadhyay,S., Stroberd, E., Duval, E., Barton, L., Hussein, I., “COVID-19: A Multidisciplinary Review”, Front. Public Health, Vol. 8, Pages 383, 2020.
2. Derosa G., Maffioli P., D’Angelo A., and Di Pierro F., “A role for quercetin in coronavirus disease 2019 (COVID-19),” Phytother. Res. PTR, Vol. 35, Issue 3, Pages 1230–1236, 2021.
3. Reuters Covid-19 Tracker “Europe: the latest coronavirus counts, charts and maps,” Reuters. https://graphics.reuters.com/world-coronavirus-tracker-and-maps/regions/europe/ September 05, 2022.
4. Sevinç, E., “An empowered AdaBoost algorithm implementation: A COVID-19 dataset study,” Comput. Ind. Eng., Vol. 165, 107912, 2022
5. Deniz A., Kiziloz, H.E., Sevinc, E., and Dokeroglu, T., “Predicting the severity of COVID-19 patients using a multi-threaded evolutionary feature selection algorithm,” Expert Syst., Vol. 39, Issue. 5, 12949, 2022
6. Karahan, M., “Yapay Sinir Ağları Metodu İle İhracat Miktarlarının Tahmini: ARIMA ve YSA Metodunun Karşılaştırmalı Analizi,” Ege Akad. Bakis Ege Acad. Rev., Vol. 15, Issue 2, Pages 165–165, Apr. 2015
7. Almasarweh, M., “ARIMA Model in Predicting Banking Stock Market Data,” Mod. Appl. Sci., Vol. 12, Issue. 11, p. 4, 2018.
8. Karahan., M., “Forecasting Amount of Export Demand with Artificial Neural Networks Method: A Comparative Analysis of ARIMA and ANN,” Ege Academic Review, Vol. 15, Issue 2, Pages 165–172, 2015.
9. Li, Z., Li, Y., “A comparative study on the prediction of the BP artificial neural network model and the ARIMA model in the incidence of AIDS,” BMC Med. Inform. Decis. Mak., Vol. 20, Issue 1, 2020 .
10. Wang, Y. W., Shen, Z. Z., Jiang, Y., “Comparison of ARIMA and GM(1,1) models for prediction of hepatitis B in China,” PloS One, Vol. 13, Issue 9, 2018.
11. Earnest, A., Evans, S.M., Sampurno, F., Millar, J., “Forecasting annual incidence and mortality rate for prostate cancer in Australia until 2022 using autoregressive integrated moving average (ARIMA) models,” BMJ Open, Vol. 9, Issue. 8, 2019
12. Yang, J., Li, L., Shi, Y., Xie, X., “An ARIMA Model With Adaptive Orders for Predicting Blood Glucose Concentrations and Hypoglycemia,” IEEE J. Biomed. Health Inform., Vol. 23, Issue. 3, Pages 1251–1260, 2019.
13. Zheng, A., Fang, Q., Zhu, Y., Jiang, C., Jin, F., Wang, X., “An application of ARIMA model for predicting total health expenditure in China from 1978-2022,” J. Glob. Health, Vol. 10, Issue. 1, 2020.
14. Li, Z., Wang, Z., Song, H., Liu, Q., He, B., Shi, P., Ji, Y., Xu, D., Wang, J., “Application of a hybrid model in predicting the incidence of tuberculosis in a Chinese population,” Infect. Drug Resist., Vol. 12, Pages 1011–1020, 2019.
15. Wang, L., Liang, C., Wu, W., Wu, S., Yang, J., Lu, X., Cai, Y., Jin, C.,, “Epidemic Situation of Brucellosis in Jinzhou City of China and Prediction Using the ARIMA Model,” Can. J. Infect. Dis. Med. Microbiol., Vol. 2019, 2019.
16. Zhai, M., Li, W., Tie, P., Wang, X., Xie, T., Ren, H., Zhang, Z., Song, W., Quan, D., Li, M., Chen, L., Qui, L., “Research on the predictive effect of a combined model of ARIMA and neural networks on human brucellosis in Shanxi Province, China: a time series predictive analysis,” BMC Infect. Dis., Vol. 21, Issue. 1, p. 280, 2021.
17. Adeyinka, D.A., Muhajarine, N., “Time series prediction of under-five mortality rates for Nigeria: comparative analysis of artificial neural networks, Holt-Winters exponential smoothing and autoregressive integrated moving average models,” BMC Med. Res. Methodol., Vol. 20, Issue 1, 2020.
18. Ryu, S., Nam, H. J., Kim, J. M., Kim, S. W., “Current and Future Trends in Hospital Utilization of Patients With Schizophrenia in Korea: A Time Series Analysis Using National Health Insurance Data,” Psychiatry Investig., Vol. 18, Issue. 8, Pages 795–800, 2021.
19. Ceylan, Z., “Estimation of COVID-19 prevalence in Italy, Spain, and France,” Sci. Total Environ., Vol. 729, 2020.
20. Fang, L., Wang, D., Pan, G., “Analysis and Estimation of COVID-19 Spreading in Russia Based on ARIMA Model,” SN Compr. Clin. Med., Vol. 2, Issue 12, Pages 2521–2527, 2020.
21. Swaraj, A., Verma, K., Kaur, A., Singh, G., Kumar, A., de Sales, L. M., “Implementation of stacking based ARIMA model for prediction of Covid-19 cases in India,” J. Biomed. Inform., Vol. 121, 2021.
22. Dinmohamed, A. G., Cellamare, M., Visser, O., de Munck, L., Elferink, M. A., Westenend, P. J., Wesseling, J., Broeders, M. J. M., Kuipers, E. J., Merkx, A. W., Nagtegaal, I. D., Siesling, S., , “The impact of the temporary suspension of national cancer screening programmes due to the COVID-19 epidemic on the diagnosis of breast and colorectal cancer in the Netherlands,” J. Hematol. Oncol.J Hematol Oncol, Vol. 13, Issue 1, 2020.
23. Dash, S., Chakraborty, C., Giri, S. K. Pani, S. K., “Intelligent computing on time-series data analysis and prediction of COVID-19 pandemics,” Pattern Recognit. Lett., Vol. 151, Pages 69–75, 2021.
24. Tulshyan, V., Sharma, D., Mittal, M., “An Eye on the Future of COVID-19: Prediction of Likely Positive Cases and Fatality in India over a 30-Day Horizon Using the Prophet Model,” Disaster Med. Public Health Prep., Pages 1–7, 2020.
25. Aydin, A., “Analysis of the effects of the Covid-19 epidemic on the Turkish air transport sector with the ARIMA model.” Ardahan Universitesi IIBF Dergisi Vol 3, Issue 2, Pages 118-127, 2021.
26. Battineni, G., Chintalapudi, N., Amenta, F., “Forecasting of COVID-19 epidemic size in four high hitting nations (USA, Brazil, India and Russia) by Fb-Prophet machine learning model,” Appl. Comput. Inform., 2020.
27. Kopanitsa, G., Metsker, O., Yakovlev, A., Fedorenko, A., Zvartau, N., “Modelling of COVID-19 Morbidity in Russia,” Stud. Health Technol. Inform., Vol. 273, Pages 262–265, 2020.
28. Talkhi, N., Fatemi, N. A., Ataei, Z., Nooghabi, M. J., “Modeling and forecasting number of confirmed and death caused COVID-19 in IRAN: A comparison of time series forecasting methods,” Biomed. Signal Process. Control, Vol. 66, 2021.
29. Djakaria I., Saleh, S. E., “Covid-19 forecast using Holt-Winters exponential smoothing,” J. Phys. Conf. Ser., Vol. 1882, Issue. 1, 2021.
30. World Health Organisation “WHO Coronavirus (COVID-19)Dashboard.” https://covid19.who.int April 28, 2022.
31. Alabdulrazzaq, H., Alenezi, M. N., Rawajfih, Y., Alghannam, B. A., Al-Hassan, A. A., Al-Anzi, F. S., “On the accuracy of ARIMA based prediction of COVID-19 spread” Results in Pyhsics, Vol. 27, 2021.
32. Taylor, S. J., Letham, B., “Forecasting at Scale,” Am. Stat., Vol. 72, Issue. 1, Pages 37–45, 2018.
33. Mahanty, M., Swathi, K. Teja, K. S., Bhattacharyya, D., “A Prophet Model to Forecast Spread of Covid-19 Pandemic,” Journal of Xidian University, Vol 14, Issue 7, Pages 949-962, 2020.
34. Panda, M., “Application of ARIMA and Holt-Winters forecasting model to predict the spreading of COVID-19 for India and its states,” medRxiv, 2020.
35. Kalekar, P. S., “Time series Forecasting using Holt-Winters Exponential Smoothing,” Time Ser. Forecast. Using Holt-Winters Exponential Smoothing” Environmental Science Jan. 2004.
36. Koehler, A. B., Snyder, R. D., Ord, J. K., “Forecasting models and prediction intervals for the multiplicative Holt-Winters method,” Int. J. Forecast., Vol. 17, Pages 269–286, 2001.
37. Satrio, C. B. A., Darmawan, W., Nadia, B. U., Hanafiah, N., “Time series analysis and forecasting of coronavirus disease in Indonesia using ARIMA model and PROPHET,” Procedia Comput. Sci., Vol. 179, Pages 524–532, 2021
38. Bögl, M., Aigner, W., Filzmoser, P., Lammarsch, T., Miksch, S., Rind, A., “Visual Analytics for Model Selection in Time Series Analysis,” IEEE Trans. Vis. Comput. Graph., Vol. 19, Issue. 12, Pages 2237–2246, 2013.
39. Akay, S., Akay, H., "Time series model for forecasting the number of COVID-19 cases in Turkey", Turkish Journal of Public Health, Vol. 19, Issue. 2, Pages 140-145, 2021.
40. Abdussalam, W., Mertel, A., Fan, K., Schüler, L., Schlechte-Wełnicz, W., Calabrese, J. M., “A scalable pipeline for COVID-19: the case study of Germany, Czechia and Poland.” arXiv, 2022.

There are 40 citations in total.

Details

Primary Language	English
Subjects	Artificial Intelligence, Software Engineering (Other)
Journal Section	Research Article
Authors	Nur Şebnem Ersöz 0000-0003-3343-9936 Pınar Güner 0000-0001-5979-0375 Ayhan Akbaş 0000-0002-6425-104X Burcu Bakir-gungor 0000-0002-2272-6270
Early Pub Date	October 14, 2022
Publication Date	December 31, 2022
Submission Date	May 25, 2022
Published in Issue	Year 2022 Volume: 6 Issue: 3

Cite

APA	Ersöz, N. Ş., Güner, P., Akbaş, A., Bakir-gungor, B. (2022). COMPARATIVE PERFORMANCE ANALYSIS OF ARIMA, PROPHET AND HOLT-WINTERS FORECASTING METHODS ON EUROPEAN COVID-19 DATA. International Journal of 3D Printing Technologies and Digital Industry, 6(3), 556-565. https://doi.org/10.46519/ij3dptdi.1120718
AMA	Ersöz NŞ, Güner P, Akbaş A, Bakir-gungor B. COMPARATIVE PERFORMANCE ANALYSIS OF ARIMA, PROPHET AND HOLT-WINTERS FORECASTING METHODS ON EUROPEAN COVID-19 DATA. IJ3DPTDI. December 2022;6(3):556-565. doi:10.46519/ij3dptdi.1120718
Chicago	Ersöz, Nur Şebnem, Pınar Güner, Ayhan Akbaş, and Burcu Bakir-gungor. “COMPARATIVE PERFORMANCE ANALYSIS OF ARIMA, PROPHET AND HOLT-WINTERS FORECASTING METHODS ON EUROPEAN COVID-19 DATA”. International Journal of 3D Printing Technologies and Digital Industry 6, no. 3 (December 2022): 556-65. https://doi.org/10.46519/ij3dptdi.1120718.
EndNote	Ersöz NŞ, Güner P, Akbaş A, Bakir-gungor B (December 1, 2022) COMPARATIVE PERFORMANCE ANALYSIS OF ARIMA, PROPHET AND HOLT-WINTERS FORECASTING METHODS ON EUROPEAN COVID-19 DATA. International Journal of 3D Printing Technologies and Digital Industry 6 3 556–565.
IEEE	N. Ş. Ersöz, P. Güner, A. Akbaş, and B. Bakir-gungor, “COMPARATIVE PERFORMANCE ANALYSIS OF ARIMA, PROPHET AND HOLT-WINTERS FORECASTING METHODS ON EUROPEAN COVID-19 DATA”, IJ3DPTDI, vol. 6, no. 3, pp. 556–565, 2022, doi: 10.46519/ij3dptdi.1120718.
ISNAD	Ersöz, Nur Şebnem et al. “COMPARATIVE PERFORMANCE ANALYSIS OF ARIMA, PROPHET AND HOLT-WINTERS FORECASTING METHODS ON EUROPEAN COVID-19 DATA”. International Journal of 3D Printing Technologies and Digital Industry 6/3 (December 2022), 556-565. https://doi.org/10.46519/ij3dptdi.1120718.
JAMA	Ersöz NŞ, Güner P, Akbaş A, Bakir-gungor B. COMPARATIVE PERFORMANCE ANALYSIS OF ARIMA, PROPHET AND HOLT-WINTERS FORECASTING METHODS ON EUROPEAN COVID-19 DATA. IJ3DPTDI. 2022;6:556–565.
MLA	Ersöz, Nur Şebnem et al. “COMPARATIVE PERFORMANCE ANALYSIS OF ARIMA, PROPHET AND HOLT-WINTERS FORECASTING METHODS ON EUROPEAN COVID-19 DATA”. International Journal of 3D Printing Technologies and Digital Industry, vol. 6, no. 3, 2022, pp. 556-65, doi:10.46519/ij3dptdi.1120718.
Vancouver	Ersöz NŞ, Güner P, Akbaş A, Bakir-gungor B. COMPARATIVE PERFORMANCE ANALYSIS OF ARIMA, PROPHET AND HOLT-WINTERS FORECASTING METHODS ON EUROPEAN COVID-19 DATA. IJ3DPTDI. 2022;6(3):556-65.