# Improvement of Time Forecasting Models Using Machine Learning for Future Pandemic Applications Based on COVID-19 Data 2020–2022

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. ARIMA Modelling

#### 2.2. Support Vector Machines Modelling

_{ε}is called the ε-intensive loss function and is formulated as follows:

#### 2.3. Least-Square Support Vector Machines Modelling

#### 2.4. Proposed Hybrid Model

#### 2.5. Proposed Algorithm

**Step 1**: Three selected time series of COVID-19 cases datasets (1 October 2020–4 November 2022), namely daily new positive cases, daily new deaths cases, and daily new recovered cases, are generated in R programming Language.**Step 2**: Each of the generated datasets is defined as $\left\{{X}_{1i}={x}_{11},{x}_{12},{x}_{13},\dots ,{x}_{n1}\right\}$, $\left\{{X}_{2i}={x}_{21},{x}_{22},{x}_{23},\dots ,{x}_{2n}\right\},$ and $\left\{{X}_{3i}={x}_{31},{x}_{32},{x}_{33},\dots ,{x}_{3n}\right\}$ for daily new positive cases, daily new deaths cases, and daily new recovered cases, respectively. Then, the best ARIMA (p, d, q) is selected after checking the autocorrelation function (ACF) plot of ARIMA (p, d, q) residuals. The best fitted value for daily new positive cases is ARIMA (2, 1, 2), while it is ARIMA (1, 1, 2) and ARIMA (0, 1, 1) for daily new fatalities cases and daily new recovered cases of COVID-19, respectively.**Step 3**: The fitted value, ${\mathcal{Y}}_{t-i}=({\mathcal{Y}}_{t-1}$, ${\mathcal{Y}}_{t-2}$, …, ${\mathcal{Y}}_{t-m})$ and the residuals ${\epsilon}_{t-i}=\left({\epsilon}_{t-1},{\epsilon}_{t-2},\dots .,{\epsilon}_{t-n}\right)$.**Step 4**: Combine the values in step 3 as a set of input variables to obtain the output ${\mathcal{Y}}_{t}$**Step 5**: The ARIMA (p, d, q) is defined by the order of q. According to the information in step 4, Vector Machines is carried out to examine the residuals to obtain the output ${L}_{t}$ using R-programming Language.**Step 6**: A fitted value of ARIMA with the hybridization of Vector Machines model is obtained for all sample data. Then, the residuals ${\epsilon}_{t}$ is generated to obtain the forecasting result $\widehat{{\mathcal{N}}_{t}}$.**Step 7**: The framing data split randomly into training data and testing data for further Vector Machines modelling. Run the Vector Machines procedure using the “e1071” and “liquidSVM” package in R-Programming Language.**Step 8**: The two modifiable parameters of the LSSVM technique (γ and σ) derived by objective function minimization such as mean square error (MSE). The grid-search method updates the parameters exponentially in the specified range using predetermined equidistant steps.**Step 9**: Assume the split data as the processing data and the order q as in Step 5. Therefore, the combine forecast as in Equation (16): ${\widehat{\mathcal{Y}}}_{\mathrm{t}}={\widehat{\ell}}_{\mathrm{t}}+\widehat{{\mathcal{N}}_{t}}$**Step 10**: Estimate the model performance using the statistical measurement which are MSE, RMSE, MAE, and MAPE.

#### 2.6. Forecasting Evaluation Criteria

## 3. Results and Discussion

#### 3.1. Application of the Hybrid Model of COVID-19 in Malaysia

#### 3.1.1. New Positive Cases Data Forecasts

#### 3.1.2. New Deaths Cases Data Forecasts

#### 3.1.3. New Recovered Cases Data Forecasts

## 4. Conclusions

## 5. Limitations and Future Recommendation

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Abdullah, M.T.; Lola, M.S.; Hisham, A.E.; Sabreena, S.; Nor Fazila, C.M.; Idham, K.; Dennis, C.Y.T. Framework of Measures for COVID-19 Pandemic in Malaysia: Threats, Initiatives and Opportunities. J. Sustain. Sci. Manag.
**2022**, 17, 8–18. [Google Scholar] [CrossRef] - Ali, M.; Khan, D.M.; Aamir, M.; Khalil, U.; Khan, Z. Forecasting COVID-19 in Pakistan. PLoS ONE
**2020**, 15, e0242762. [Google Scholar] [CrossRef] [PubMed] - WHO. Coronavirus Disease (COVID-19) in Malaysia. 2020. Available online: https://www.who.int/malaysia/emergencies/coronavirus-disease-(COVID-19)-in-Malaysia (accessed on 23 May 2020).
- KKM. COVID-19 Malaysia: Situasi Terkini 25 Oktober 2020. 2020. Available online: https://covid-19.moh.gov.my/terkini (accessed on 25 June 2022).
- Gecili, E.; Ziady, A.; Szczesniak, R.D. Forecasting COVID-19 confirmed cases, deaths and recoveries: Revisiting established time series modeling through novel applications for the USA and Italy. PLoS ONE
**2021**, 16, e0244173. [Google Scholar] [CrossRef] - Awwad, F.A.; Mohamoud, M.A.; Abonazel, M.R. Estimating COVID-19 cases in Makkah region of Saudi Arabia: Space-time ARIMA modeling. PLoS ONE
**2021**, 16, e0250149. [Google Scholar] [CrossRef] - Sahai, A.K.; Rath, N.; Sood, V.; Singh, M.P. ARIMA modelling & forecasting of COVID-19 in top five affected countries. Diabetes Metab. Syndr. Clin. Res. Rev.
**2020**, 14, 1419–1427. [Google Scholar] [CrossRef] - Alzahrani, S.I.; Aljamaan, I.A.; Al-Fakih, E.A. Forecasting the Spread Of The COVID-19 Pandemic In Saudi Arabia Using ARIMA Prediction Model Under Current Public Health Interventions. J. Infect. Public Health.
**2020**, 13, 914–919. [Google Scholar] [CrossRef] - Benvenuto, D.; Giovanetti, M.; Vassallo, L.; Angeletti, S.; Ciccozzi, M. Application of the ARIMA model on the COVID-2019 epidemic dataset. Data Brief
**2020**, 29, 105340. [Google Scholar] [CrossRef] - Ceylan, Z. Estimation of COVID-19 prevalence in Italy, Spain, and France. Sci. Total Environ.
**2020**, 729, 138817. [Google Scholar] [CrossRef] - Hernandez-Matamoros, A.; Fujita, H.; Hayashi, T.; Perez-Meana, H. Forecasting of COVID19 per regions using ARIMA models and polynomial functions. Appl. Soft Comput.
**2020**, 96, 106610. [Google Scholar] [CrossRef] - Khan, F.M.; Gupta, R. ARIMA and NAR based prediction model for time series analysis of COVID-19 cases in India. J. Saf. Sci. Resil.
**2020**, 1, 12–18. [Google Scholar] [CrossRef] - Kayode, O.; Fahimah, A.; Mustapha, R.; Jacques, D. Data Analysis and Forecasting of COVID-19 Pandemic in Kuwait Based on Daily Observation and Basic Reproduction Number Dynamics. Kuwait J. Sci. Special Issue
**2021**, 1–30. [Google Scholar] [CrossRef] - Rahman, M.S.; Chowdhury, A.H.; Amrin, M. Accuracy comparison of ARIMA and XGBoost forecasting models in predicting the incidence of COVID-19 in Bangladesh. PLoS Glob. Public Health
**2022**, 2, e0000495. [Google Scholar] [CrossRef] - Aisyah, W.I.W.M.N.; Muhamad Safiih, L.; Razak, Z.; Nurul Hila, Z.; Abd Aziz, K.A.H.; Elayaraja, A.; Nor Shairah, A.Z. Improved of Forecasting Sea Surface Temperature based on Hybrid ARIMA and Vector Machines Model. Malays. J. Fundam. Appl. Sci.
**2021**, 17, 609–620. [Google Scholar] [CrossRef] - Nurul Hila, Z.; Muhamad Safiih, L.; Maman Abdurachman, D.; Fadhilah, Y.; Mohd Noor Afiq, R.; Aziz, D.; Yahaya, I.; Mohd Tajuddin, A. Improvement of Time Forecasting Models using A Novel Hybridization of Bootstrap and Double Bootstrap Artificial Neural Networks. Appl. Soft Comput. J.
**2019**, 84, 105676. [Google Scholar] [CrossRef] - Lee, M.C. Using support vector machine with a hybrid feature selection method to the stock trend prediction. J. Expert Syst. Appl.
**2009**, 36, 10896–10904. [Google Scholar] [CrossRef] - Vapnik, V.N. The Nature of Statistical Learning Theory, 1st ed.; Springer: New York, NY, USA, 1995. [Google Scholar]
- Sudheer, C.; Maheswaran, R.; Panigrahi, B.K.; Mathur, S. A hybrid SVM-PSO model for forecasting monthly streamflow. Neural Comput. Appl.
**2013**, 24, 1381–1389. [Google Scholar] [CrossRef] - Chakraborty, T.; Chakraborty, A.K.; Biswas, M.; Banerjee, S.; Bhattacharya, S. Unemployment Rate Forecasting: A Hybrid Approach. Comput. Econ.
**2020**, 57, 183–201. [Google Scholar] [CrossRef] - Zhang, G.P. Time series forecasting using a hybrid ARIMA and Neural Network Model. Neurocomputing
**2003**, 50, 159–175. [Google Scholar] [CrossRef] - Terui, N.; Van Dijk, H. Combined forecasts from linear and nonlinear time series models. Int. J. Forecast.
**2002**, 18, 421–438. [Google Scholar] [CrossRef][Green Version] - Wang, X.; Meng, M. A Hybrid Neural Network and ARIMA Model for Energy Consumption Forecasting. J. Comput.
**2012**, 7, 1184–1190. [Google Scholar] [CrossRef] - Muhamad Safiih, L.; Nurul Hila, Z.; Mohd Tajuddin, A.; Vigneswary, P.; Mohd Noor Afiq, R.; Razak, Z.; Suffian, I.; Khalili, I. Improving the Performance of ANN-ARIMA Models for Predicting Water Quality in The Offshore Area of Kuala Terengganu, Terengganu, Malaysia. J. Sustain. Sci. Manag.
**2018**, 13, 27–37. [Google Scholar] - Pai, P.F.; Lin, C.-S. A hybrid ARIMA and Support Vector Machines Model in Stock Price Forecasting. Int. J. Manag. Sci.
**2005**, 3, 497–505. [Google Scholar] [CrossRef] - Lee, N.-U.; Shim, J.-S.; Ju, Y.-W.; Park, S.-C. Design and Implementation of the SARIMA–SVM time series analysis algorithm for the improvement of atmospheric environment forecast accuracy. Soft Comput.
**2017**, 22, 4275–4281. [Google Scholar] [CrossRef] - Hao, Y.; Xu, T.; Hu, H.; Wang, P.; Bai, Y. Prediction and analysis of Corona Virus Disease 2019. PLoS ONE
**2020**, 15, e0239960. [Google Scholar] [CrossRef] [PubMed] - Roy, S.; Ghosh, P. Factors affecting COVID-19 infected and death rates inform lockdown- related policymaking. PLoS ONE
**2020**, 15, e0241165. [Google Scholar] [CrossRef] [PubMed] - Mahdavi, M.; Choubdar, H.; Zabeh, E.; Rieder, M.; Safavi-Naeini, S.; Jobbagy, Z.; Ghorbani, A.; Abedini, A.; Kiani, A.; Khanlarzadeh, V.; et al. A machine learning based exploration of COVID-19 mortality risk. PLoS ONE
**2021**, 16, e0252384. [Google Scholar] [CrossRef] - Singhal, T. A Review of Coronavirus Disease-2019 (COVID-19). Indian J. Pediatr.
**2020**, 87, 281–286. [Google Scholar] [CrossRef][Green Version] - Qu, Z.; Li, Y.; Jiang, X.; Niu, C. An innovative ensemble model based on multiple neural networks and a novel heuristic optimization algorithm for COVID-19 forecasting. Expert Syst. Appl.
**2023**, 212, 118746. [Google Scholar] [CrossRef] - Zivkovic, M.; Bacanin, N.; KVenkatachalam Nayyar, A.; Djordjevic, A.; Strumberger, I.; Al-Turjman, F. COVID-19 cases prediction by using hybrid machine learning and beetle antennae search approach. Sustain. Cities Soc.
**2021**, 66, 102669. [Google Scholar] [CrossRef] - Melin, P.; Sánchez, D.; Castro, J.R.; Castillo, O. Design of Type-3 Fuzzy Systems and Ensemble Neural Networks for COVID-19 Time Series Prediction Using a Firefly Algorithm. Axioms
**2022**, 11, 410. [Google Scholar] [CrossRef] - Sarah, M. The Future of Pandemics. News-Medical. Available online: https://www.news-medical.net/health/The-Future-of-Pandemics.aspx (accessed on 17 January 2022).
- Suykens, J.A.K.; Vandewalle, J. Least Squares Support Vector Machine Classifiers. Neural Process. Lett.
**1999**, 9, 293–300. [Google Scholar] [CrossRef] - Naeem, M.; Yu, J.; Aamir, M.; Khan, S.A.; Adeleye, O.; Khan, Z. Comparative analysis of machine learning approaches to analyse and predict the COVID-19 outbreak. Peer J. Comput. Sci.
**2021**, 17, e746. [Google Scholar] [CrossRef] [PubMed] - Qiang, X.; Aamir, M.; Naeem, M.; Ali, S.; Aslam, A.; Shao, Z. Analysis and Forecasting COVID-19 Outbreak in Pakistan Using Decomposition and Ensemble Model. Comput. Mater. Contin.
**2021**, 68, 842–856. [Google Scholar] [CrossRef] - Adhikari, S.P.; Meng, S.; Wu, Y.-U.; Mao, Y.-P.; Ye, R.-X.; Wang, Q.-Z.; Sun, C.; Sylvia, S.; Rozelle, S.; Raat, H.; et al. Epidemiology, causes, clinical manifestation and diagnosis, prevention and control of coronavirus disease (COVID-19) during the early outbreak period: A scoping review. Infect. Dis. Poverty
**2020**, 9, 29. [Google Scholar] [CrossRef] [PubMed][Green Version] - Ahmadini, A.A.H.; Naeem, M.; Aamir, M.; Dewan, R.; Alshqaq, S.S.A.; Mashwani, W.K. Analysis and Forecast of the Number of Deaths, Recovered Cases, and Confirmed Cases from COVID-19 for the Top Four Affected Countries Using Kalman Filter. Front. Phys.
**2021**, 9, 629320. [Google Scholar] [CrossRef] - Alessa, A.A.; Alotaibie, T.M.; Elmoez, Z.; Alhamad, H.E. Impact of COVID-19 on Entrepreneurship and Consumer Behaviour: A Case Study in Saudi Arabia. J. Asian Financ. Econ. Bus.
**2021**, 8, 201–210. [Google Scholar] [CrossRef] - Huck, N. Pairs trading and outranking: The multi-step-ahead forecasting case. Eur. J. Oper. Res.
**2010**, 207, 1702–1716. [Google Scholar] [CrossRef] - Nisbet, R.; Elder JMiner, G. Chapter 11—Model Evaluation and Enhancement. In Handbook of Statistical Analysis and Data Mining Applications; Academic Press: Cambridge, MA, USA, 2018; pp. 215–233. [Google Scholar] [CrossRef]
- Nurul Hila, Z.; Muhamad Safiih, L. The Performance of BB-MCEWMA Model: Case Study on Sukuk Rantau Abang Capital Berhad, Malaysia. Int. J. Appl. Bus. Econ. Res.
**2016**, 14, 63–77. [Google Scholar] - Nurul Hila, Z.; Muhamad Safiih, L.; Nur Shazrahanim, K. Modelling Moving Centreline Exponentially Weighted Moving Average (MCEWMA) with bootstrap approach: Case study on sukuk musyarakah of Rantau Abang Capital Berhad, Malaysia. Int. J. Appl. Bus. Econ. Res.
**2016**, 14, 621–638. [Google Scholar] - Muhamad Safiih, L.; Nurul Hila, Z.; Mohd Noor Afiq, R.; Hizir, S. Double Bootstrap Control Chart for Monitoring SUKUK Volatility at Bursa Malaysia. J. Teknol.
**2017**, 79, 149–157. [Google Scholar] [CrossRef][Green Version]

**Figure 3.**Results obtained from the proposed model for daily new positive COVID-19 cases dataset: (

**a**) actual data vs. ARIMA model, (

**b**) actual data vs. LSSVM models, (

**c**) actual data vs. SVM model, (

**d**) actual data vs. ARIMA–SVM models, (

**e**) actual data vs. ARIMA–LSSVM models.

**Figure 4.**Models’ prediction of daily new positive COVID-19 cases dataset (20% test sample): (

**a**) actual data vs. ARIMA model, (

**b**) actual data vs. SVM model, (

**c**) actual data vs. LSSVM models, (

**d**) actual data vs. ARIMA–SVM models, (

**e**) actual data vs. ARIMA–LSSVM models.

**Figure 5.**Actual and three weeks ahead forecasted values of ARIMA, SVM, LSSVM, ARIMA–SVM, and ARIMA–LSSVM models for new cases of COVID-19 of the 80% training and 20% testing set.

**Figure 7.**Results obtained from the proposed model for daily new death COVID-19 cases dataset: (

**a**) actual data vs. ARIMA model, (

**b**) actual data vs. LSSVM models, (

**c**) actual data vs. SVM model, (

**d**) actual data vs. ARIMA–SVM models, (

**e**) actual data vs. ARIMA–LSSVM models.

**Figure 8.**Models’ prediction of daily new death COVID-19 cases dataset (20% test sample): (

**a**) actual data vs. ARIMA model, (

**b**) actual data vs. SVM model, (

**c**) actual data vs. LSSVM models, (

**d**) actual data vs. ARIMA–SVM models, (

**e**) actual data vs. ARIMA–LSSVM models.

**Figure 9.**Actual and three-weeks-ahead forecasted values of ARIMA, SVM, LSSVM, ARIMA–SVM and ARIMA–LSSVM models for daily new deaths COVID-19 cases of the 80% training and 20% testing set.

**Figure 11.**Results obtained from the proposed model for daily new recovered COVID-19 cases dataset: (

**a**) actual data vs. ARIMA model, (

**b**) actual data vs. LSSVM models, (

**c**) actual data vs. SVM model, (

**d**) actual data vs. ARIMA–SVM models, (

**e**) actual data vs. ARIMA–LSSVM models.

**Figure 12.**Models’ prediction of daily new recovered COVID-19 cases dataset (20% test sample): (

**a**) actual data vs. ARIMA model, (

**b**) actual data vs. SVM model, (

**c**) actual data vs. LSSVM models, (

**d**) actual data vs. ARIMA–SVM models, (

**e**) actual data vs. ARIMA–LSSVM models.

**Figure 13.**Actual and three weeks ahead forecasted values of ARIMA, SVM, LS–SVM, ARIMA–SVM and ARIMA–LSSVM models for daily new recovered COVID-19 cases of the 80% training and 20% testing set.

**Table 1.**Descriptive statistics of COVID-19 daily new cases, death, and recovered cases of Malaysia.

New Case | New Death | New Recovered | |
---|---|---|---|

Min | 2.60000 × 10^{2} | 0 | 1.8 |

1st Qu | 1.9220 × 10^{3} | 4 | 1.8430 × 10^{3} |

Median | 3.4710 × 10^{3} | 11 | 3.4470 × 10^{3} |

Mean | 6.4155 × 10^{3} | 47.5098 | 6.3227 × 10^{3} |

3rd Qu | 6.8240 × 10^{3} | 58 | 6.7750 × 10^{3} |

Max | 3.3406 × 10^{4} | 592 | 3.3872 × 10^{4} |

SD | 7.0978 × 10^{3} | 81.1215 | 7.0583 × 10^{3} |

COVID-19 Daily Cases | ARIMA (p, d, q) | AIC | BIC |
---|---|---|---|

Daily New Positive Cases | (2, 1, 2) | 12,564.54 | 12,587.73 |

Daily New Deaths Cases | (1, 1, 2) | 6930.12 | 6948.63 |

Daily New Recovered Cases | (0, 1, 1) | 13,044.74 | 13,054.01 |

Model Parameters | Estimate | Z-Stat | p-Value |
---|---|---|---|

New Case ARIMA (2, 1, 2) | |||

${\theta}_{1}$ | 1.2408 | 120.085 | 2.2 × 10^{−16} |

${\theta}_{2}$ | −0.9715 | −98.320 | 2.2 × 10^{−16} |

${\phi}_{1}$ | −1.2628 | −42.225 | 2.2 × 10^{−16} |

${\phi}_{2}$ | 0.8738 | 48.102 | 2.2 × 10^{−16} |

Recovered Case ARIMA (0, 1, 1) | 2.2 × 10^{−16} | ||

${\phi}_{1}$ | −0.3473 | −9.953 | 2.2 × 10^{−16} |

Death Case ARIMA (1, 1, 2) | 2.2 × 10^{−16} | ||

${\theta}_{1}$ | 0.8595 | 19.852 | 2.2 × 10^{−16} |

${\phi}_{1}$ | −1.6196 | −35.651 | 2.2 × 10^{−16} |

${\phi}_{2}$ | 0.7039 | 20.432 | 2.2 × 10^{−16} |

COVID-19 Daily Cases | LSSVM Parameter | MSE |
---|---|---|

γ = 11, σ = 0.008 | 11,432,512 | |

γ = 38, σ = 0.008 | 10,235,488 | |

Daily New Positive Cases | γ = 74, σ = 0.008 | 9,025,413 |

γ = 110, σ = 0.008 | 8,014,123 | |

γ = 264, σ = 0.008 | 6,661,412 | |

γ = 25, σ = 0.006 | 1678.364 | |

γ = 56, σ = 0.006 | 1233.481 | |

Daily New Deaths Cases | γ = 277, σ = 0.006 | 965.143 |

γ = 436, σ = 0.006 | 554.368 | |

γ = 877, σ = 0.006 | 250.887 | |

γ = 54, σ = 0.008 | 28,412,113 | |

γ = 89, σ = 0.008 | 27,140,039 | |

Daily New Recovered Cases | γ = 125, σ = 0.008 | 26,412,142 |

γ = 275, σ = 0.008 | 23,032,256 | |

γ = 334, σ = 0.008 | 21,114,252 |

MODELS | TRAIN | TEST | ||||
---|---|---|---|---|---|---|

MSE | MAE | MSE | MAPE | RMSE | MAE | |

ARIMA | 929,843.169 | 611.0274 | 298,988.28 | 0.15167 | 546.7982 | 397.57 |

SVM | 8,355,184.483 | 2001.644 | 274,588.16 | 0.15421 | 524.0116 | 390.3848 |

LSSVM | 1084.1527 | 739.5387 | 83,026.550 | 0.07580 | 288.1432 | 205.6450 |

ARIMA–SVM | 42,552.7137 | 90.34845 | 61,223.474 | 0.05633 | 247.4337 | 146.9841 |

ARIMA–LSSVM | 10,634.1142 | 46.54471 | 25,478.114 | 0.01547 | 159.6182 | 75.6987 |

**Table 6.**Percentage improvement of the proposed models with other forecasting models (the COVID-19 cases of daily new positive cases).

Model | MAE | MAPE | MSE | RMSE |
---|---|---|---|---|

ARIMA | 80.9596549 | 89.80022417 | 91.47855762 | 70.80857252 |

SVM | 80.60920917 | 89.96822515 | 90.72133554 | 69.53918577 |

LSSVM | 63.18962289 | 79.59102902 | 69.31329316 | 44.60455773 |

ARIMA–SVM | 48.49871517 | 72.5368365 | 58.38505669 | 35.49051726 |

MODELS | TRAIN | TEST | ||||
---|---|---|---|---|---|---|

MSE | MAE | MSE | MAPE | RMSE | MAE | |

ARIMA | 697.999 | 11.8083 | 6.06741 | 0.56838 | 2.46321 | 1.92791 |

SVM | 1409.19 | 21.8006 | 5.38920 | 0.53687 | 2.32146 | 1.85605 |

LSSVM | 505.181 | 11.4309 | 5.38920 | 0.53687 | 2.32146 | 1.85605 |

ARIMA–SVM | 49.4459 | 3.53812 | 0.92630 | 0.19088 | 0.96303 | 0.76230 |

ARIMA–LSSVM | 19.6422 | 1.03218 | 0.89114 | 0.18741 | 0.94400 | 0.72364 |

**Table 8.**Percentage improvement of the proposed models with other forecasting models (the COVID-19 cases of daily new death cases).

Model | MAE | MAPE | MSE | RMSE |
---|---|---|---|---|

ARIMA | 62.46505283 | 67.02734086 | 85.31267872 | 61.67602437 |

SVM | 61.60592539 | 66.73588924 | 83.92334934 | 59.90434808 |

LSSVM | 61.01182619 | 65.09210796 | 83.46433608 | 59.33593514 |

ARIMA–LSSVM | 5.071494162 | 1.81789606 | 3.795746518 | 1.976054744 |

**Table 9.**Performance measures of the proposed model for daily new recovered COVID-19 cases datasets.

MODELS | TRAIN | TEST | ||||
---|---|---|---|---|---|---|

MSE | MAE | MSE | MAPE | RMSE | MAE | |

ARIMA | 1,802,678.36 | 804.4378 | 271,462.22 | 0.1560 | 521.0203 | 387.2768 |

SVM | 7,636,804.13 | 1890.917 | 239,672.00 | 0.1504 | 489.5630 | 371.6573 |

LSSVM | 1,206,113.52 | 723.9413 | 149,871.53 | 0.1127 | 387.1324 | 285.9190 |

ARIMA–SVM | 99,205.699 | 136.8519 | 26,108.02 | 0.0396 | 161.5797 | 104.1002 |

ARIMA–LSSVM | 47,602.551 | 80.2214 | 13,004.11 | 0.0125 | 114.0351 | 54.14471 |

**Table 10.**Percentage improvement of the proposed models with other forecasting models (the COVID-19 cases of daily new recovered cases).

Model | MAE | MAPE | MSE | RMSE |
---|---|---|---|---|

ARIMA | 86.01911863 | 91.98717949 | 95.20960596 | 78.11311767 |

SVM | 85.43154944 | 91.68882979 | 94.57420558 | 76.70675684 |

LSSVM | 81.06291992 | 88.90860692 | 91.32316191 | 70.54364347 |

ARIMALSSVM | 47.98789051 | 68.43434343 | 50.19112901 | 29.42485968 |

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## Share and Cite

**MDPI and ACS Style**

K Abdul Hamid, A.A.; Wan Mohamad Nawi, W.I.A.; Lola, M.S.; Mustafa, W.A.; Abdul Malik, S.M.; Zakaria, S.; Aruchunan, E.; Zainuddin, N.H.; Gobithaasan, R.U.; Abdullah, M.T. Improvement of Time Forecasting Models Using Machine Learning for Future Pandemic Applications Based on COVID-19 Data 2020–2022. *Diagnostics* **2023**, *13*, 1121.
https://doi.org/10.3390/diagnostics13061121

**AMA Style**

K Abdul Hamid AA, Wan Mohamad Nawi WIA, Lola MS, Mustafa WA, Abdul Malik SM, Zakaria S, Aruchunan E, Zainuddin NH, Gobithaasan RU, Abdullah MT. Improvement of Time Forecasting Models Using Machine Learning for Future Pandemic Applications Based on COVID-19 Data 2020–2022. *Diagnostics*. 2023; 13(6):1121.
https://doi.org/10.3390/diagnostics13061121

**Chicago/Turabian Style**

K Abdul Hamid, Abdul Aziz, Wan Imanul Aisyah Wan Mohamad Nawi, Muhamad Safiih Lola, Wan Azani Mustafa, Siti Madhihah Abdul Malik, Syerrina Zakaria, Elayaraja Aruchunan, Nurul Hila Zainuddin, R.U. Gobithaasan, and Mohd Tajuddin Abdullah. 2023. "Improvement of Time Forecasting Models Using Machine Learning for Future Pandemic Applications Based on COVID-19 Data 2020–2022" *Diagnostics* 13, no. 6: 1121.
https://doi.org/10.3390/diagnostics13061121