A Time Series Forecast of COVID-19 Infections, Recoveries and Fatalities in Nigeria
Abstract
:1. Introduction
2. Literature Review
2.1. Coronavirus
2.2. Time Series Models
2.2.1. Autoregressive (AR) Models, Moving Average (MA) Models, and the Autoregressive Integrated Moving Average (ARIMA) Models
2.2.2. Vector Autoregressive Model (VAR)
2.2.3. Vector Error Correction (VEC) Model
2.2.4. Autoregressive Distributed Lag System (ARDL)
2.3. Theoretical Framework
2.4. Empirical Review
- H01 The COVID-19 infections in Nigeria are not related to time
- H02 The COVID-19 infections and fatalities in Nigeria are not significantly related to the recoveries
- H03 The COVID-19 infections and recoveries in Nigeria are not significant related to the fatalities
3. Methodology
3.1. Measurement of Variables
3.2. Method of Data Analysis
3.2.1. Model Specifications
- CINF = infectious cases of COVID-19
- TM = the time (days) from May to August 2020
- CRCV = COVID-19 recoveries from confirmed cases
- CFT = COVID-19 fatalities from confirmed cases
- = Part of the changes experienced in COVID-19 infections that is not traceable to the changes in time
- = Part of the changes in COVID-19 infections that variation in time can account for
- = The portion of the changes in COVID-19 recoveries that cannot be traced to the changes in the independent variables
- − = coefficients of the independent variables
- = the aspect of the changes in COVID-19 deaths that is not caused by the independent variables
- − = coefficients of the independent variables
- e = Random error associated with the measurement of the variables.
- is the “change in” is the change of differencing operator,
- (i =1, 3, … 5) = represents the number of lags,
- is the error term.
3.2.2. Test for Normality and Significance of Forecast Errors
4. Findings
4.1. Stationarity and Cointegration Tests
4.2. Estimation of the Infections, Recoveries and Fatalities of COVID-19
4.3. Discussion of Findings
4.4. Implications for Policy
5. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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S/N | Variable | p Value at Level | p Value at First Diff. | Significant at |
---|---|---|---|---|
1 | Infections | 0.9917 | 0.030 | First Difference |
2 | Recoveries | 0.7877 | <0.01 | First Difference |
3 | Fatalities | 0.3745 | <0.01 | First Difference |
Hypothesized | 0.05 | |||
---|---|---|---|---|
Number of Coffs. | Eigenvalue | Trace | Critical Value | Sig. Prob |
None | 0.4253 | 113.8462 | 95.7537 | 0.0016 ** |
At most 1 | 0.3738 | 78.9463 | 61.8189 | 0.0078 ** |
At most 2 | 0.3097 | 49.4564 | 47.8561 | 0.0352 * |
Variable | Coefficient | Standard Error | t | Sig P |
---|---|---|---|---|
Infections | (−1) 0.963 | 0.0101 | 9.795 | 0.000 ** |
Time (T) | 19.8419 | 4.8778 | 4.068 | 0.0001 ** |
C | 195.17 | 49.949 | 3.91 | 0.0002 * |
Adjusted R-square | 0.9960 | Durbin-Watson Statistic | 1.8634 |
Variable | Coefficient | Standard Error | t | Sig P |
---|---|---|---|---|
COVID-19 Recoveries | (−1) 0.93 | 0.0310 | 30.2649 | 0.000 ** |
COVID-19 Infections | 0.2082 | 0.0964 | 2.1596 | 0.033 * |
COVID-19 Fataliti | −7.869 | 4.3629 | −1.8037 | 0.074 |
C | 381.40 | 376.39 | 1.0156 | 0.3120 |
Adjusted R-square | 0.9237 | Durbin-Watson Statistic | 2.0539 |
Variable | Coefficient | Standard Error | t | Sig P |
---|---|---|---|---|
COVID-19 Fatalities | (−1) 1.0373 | 0.0256 | 16.53 | 0.000 ** |
COVID-19 Infections | −0.00066 | 0.0056 | 1.173 | 0.2434 |
COVID-19 Recoveries | −0.000122 | 0.00017 | −0.734 | 0.4646 |
C | 14.706 | 1.9607 | 2.911 | 0.0044 ** |
Adjusted R-square | 0.9864 | Durbin-Watson Statistic | 1.9419 |
T | Date | Forecasted Infections CI = 195.17 + 0.963CI (−1) + 19.84T | Actual Infections | Deviation | % Change | Absolute % Change |
---|---|---|---|---|---|---|
1932 | ||||||
1 | 01/05 | 2147 | 2170 | −23 | −1.1 | 1.1 |
7 | 07/05 | 3363 | 3526 | −163 | −4.6 | 4.6 |
14 | 14/05 | 5087 | 5162 | −75 | −2.37 | 2.37 |
21 | 21/05 | 7042 | 7016 | 26 | 0.37 | 0.37 |
28 | 28/05 | 9161 | 8915 | 246 | 2.76 | 2.76 |
31 | 31/05 | 10,300 | 10,162 | 136 | 1.36 | 1.36 |
32 | 01/06 | 10,597 | 10,578 | 19 | 0.18 | 0.18 |
38 | 07/06 | 12,730 | 12,846 | −116 | −0.9 | 0.9 |
45 | 14/06 | 16,190 | 16,085 | 105 | 0.65 | 0.65 |
52 | 21/06 | 20,302 | 20,244 | 56 | 0.29 | 0.29 |
59 | 28/06 | 24,551 | 24,567 | −16 | −0.07 | 0.07 |
61 | 30/06 | 25,609 | 25,694 | −85 | −0.33 | 0.33 |
62 | 01/07 | 26,169 | 26,484 | −315 | −1.19 | 1.19 |
68 | 07/07 | 29,471 | 29,789 | −318 | −1.07 | 1.07 |
75 | 14/07 | 33,610 | 33,616 | −6 | −0.018 | 0.018 |
82 | 21/07 | 37,670 | 37,801 | −131 | −0.35 | 0.35 |
89 | 28/07 | 41,617 | 41,804 | −187 | −0.45 | 0.45 |
92 | 31/07 | 43,130 | 43,151 | −21 | −0.05 | 0.05 |
93 | 01/08 | 43,595 | 43,537 | 58 | 0.13 | 0.13 |
99 | 07/08 | 45,729 | 45,687 | 42 | 0.092 | 0.092 |
106 | 14/08 | 48,634 | 48,445 | 189 | 0.39 | 0.39 |
113 | 21/08 | 51,516 | 51,304 | 212 | 0.41 | 0.41 |
Date | Forecasted Recoveries CR = 381.4 + 0.96CR(−1) +0.21CI−7.87CF | Actual Recoveries | Infections | Fatalities | Dev. | % Δ | |% Δ| |
---|---|---|---|---|---|---|---|
319 | |||||||
01/05 | 539 | 352 | 2170 | 68 | 187 | 53 | 53 |
07/05 | 607 | 601 | 3526 | 107 | 6 | 0.991 | 0.99 |
14/05 | 1146 | 1180 | 5162 | 167 | −33.77 | −2.86 | 2.86 |
21/05 | 1853 | 1907 | 7016 | 211 | −54 | 0.03 | 0.03 |
28/05 | 2542 | 2501 | 8915 | 259 | 40 | 1.6 | 1.6 |
31/05 | 3023 | 3007 | 10,162 | 287 | 16 | 0.53 | 0.53 |
01/06 | 3141 | 3122 | 10,578 | 299 | 19 | 0.61 | 0.61 |
07/06 | 3946 | 3959 | 12,846 | 354 | −13 | −0.33 | 0.33 |
14/06 | 5216 | 5220 | 16,085 | 420 | −5 | −0.096 | 0.096 |
21/06 | 6804 | 6879 | 20,244 | 518 | −75 | −1.09 | 1.09 |
28/06 | 9115 | 9007 | 24,567 | 565 | 108.17 | 1.2 | 1.2 |
30/06 | 9878 | 9746 | 25,694 | 590 | 132 | 1.4 | 1.4 |
01/07 | 10,258 | 10,152 | 26,484 | 603 | 106 | 1.04 | 1.04 |
07/07 | 12,532 | 12,108 | 29,789 | 669 | 424 | 3.5 | 3.5 |
14/07 | 13,752 | 13,792 | 33,616 | 754 | −39.91 | −0.29 | 0.29 |
21/07 | 16,244 | 15,677 | 37,801 | 805 | 567 | 3.62 | 3.62 |
28/07 | 19,258 | 18,764 | 41,804 | 869 | 534 | 2.85 | 2.85 |
31/07 | 20,446 | 19,565 | 43,151 | 879 | 881 | 4.5 | 4.5 |
01/08 | 20,389 | 20,087 | 43,537 | 883 | 302 | 1.5 | 1.5 |
07/08 | 32,769 | 32,637 | 45,687 | 936 | 132 | 0.41 | 0.41 |
14/08 | 34,805 | 35,998 | 48,445 | 973 | −1193 | −3.31 | 3.31 |
21/08 | 38,256 | 37,885 | 51,304 | 996 | 371 | 0.98 | 0.98s |
Date | Forecasted Fatalities CR = 14.5 + 0.90CF (−1) +0.0024CI − 0.0008CR | Actual Fatalities | Recoveries | Infections | Dev. | % Δ | |% Δ| |
---|---|---|---|---|---|---|---|
58 | |||||||
01/05 | 66 | 68 | 352 | 2170 | −2 | −2.94 | 2.94 |
07/05 | 110 | 107 | 601 | 3526 | 3 | 2.8 | 2.8 |
14/05 | 173 | 167 | 1180 | 5162 | 6 | 3.6 | |
21/05 | 205 | 211 | 1907 | 7016 | −6 | −2.84 | 2.84 |
28/05 | 363 | 259 | 2501 | 8915 | 4 | 1.54 | 1.54 |
31/05 | 276 | 287 | 3007 | 10,162 | −11 | −3.83 | 3.83 |
01/06 | 296 | 299 | 3122 | 10,578 | −3 | −1 | 1 |
07/06 | 352 | 354 | 3959 | 12,846 | −2 | −0.56 | 0.56 |
14/06 | 417 | 420 | 5220 | 16,085 | −3 | −0.71 | 0.71 |
21/06 | 518 | 518 | 6879 | 20,244 | 0 | 0 | 0 |
28/06 | 568 | 565 | 9007 | 24,567 | 3 | 0.53 | 0.53 |
30/06 | 582 | 590 | 9746 | 25,694 | −8 | −1.4 | 1.4 |
01/07 | 600 | 603 | 10,152 | 26,484 | −3 | −0.50 | 0.50 |
07/07 | 670 | 669 | 12,108 | 29,789 | 1 | 0.15 | 0.15 |
14/07 | 754 | 754 | 13,792 | 33,616 | 0 | 0 | 0 |
21/07 | 810 | 805 | 15,677 | 37,801 | 5 | 0.62 | 0.62 |
28/07 | 869 | 869 | 18,764 | 41,804 | 0 | 0 | 0 |
31/07 | 886 | 879 | 19,565 | 43,151 | 7 | 0.80 | 0.80 |
01/08 | 887 | 883 | 20,087 | 43,537 | 4 | 0.45 | 0.45 |
07/08 | 937 | 936 | 32,637 | 45,687 | 1 | 0.11 | 0.11 |
14/08 | 972 | 973 | 35,998 | 48,445 | −1 | −0.1 | 0.1 |
21/08 | 997 | 996 | 37,885 | 51,304 | 1 | 0.1 | 0.1 |
Variable | Z | Significant P | Remark |
---|---|---|---|
Infections | 0.561 | 0.911 | Normal |
Recoveries | 1.261 | 0.083 | Normal |
Fatalities | 0.599 | 0.865 | Normal |
Variable | Mean | t | Significant P | Remark |
---|---|---|---|---|
Infections | −16.682 | −0.517 | 0.610 | Not Significant |
Recoveries | 109.61 | 1.348 | 0.192 | Not Significant |
Fatalities | −0.061 | 1.191 | 0.850 | Not Significant |
Box Ljung Statistic and Asymptotic Probabilities | ||||
---|---|---|---|---|
Variable | Lag 1 | Lag 2 | Lag 3 | Lag 4 |
COVID-19 Infections | 0.094 (0.76) | 2.95 (0.23) | 3.01 (0.31) | 3.22 (0.52) |
COVID-19 Recoveries | 0.23 (0.63) | 0.62 (0.73) | 2.74 (0.48) | 2.51 (0.64) |
COVID-19 Fatalities | 0.06 (0.81) | 1.45 (0.49) | 1.52 (0.68) | 2.25 (0.69) |
COVID-19 Infection | COVID-19 Recoveries | COVID-19 Fatalities | ||
---|---|---|---|---|
October: | Actual | 62,853 | 58,675 | 1144 |
Forecast | 59,969 | 52,791 | 1099 | |
Deviation | −2884 (−4.59%) | −5904 (−10.06%) | −45 (−3.93%) | |
November: | Actual | 67,557 | 63,282 | 1173 |
Forecast | 65,216 | 54,767 | 1265 | |
Deviation | −2341 (−2.47%) | −8515 (−13.5%) | 92 (7.8%) | |
December: | Actual | 86,576 | 73,322 | 1278 |
Forecast | 71,067 | 67,509 | 1314 | |
Deviation | 15,509 (17.9%) | 5813 (7.9%) | 36 (2.03%) |
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Inegbedion, H.E. A Time Series Forecast of COVID-19 Infections, Recoveries and Fatalities in Nigeria. Sustainability 2023, 15, 7324. https://doi.org/10.3390/su15097324
Inegbedion HE. A Time Series Forecast of COVID-19 Infections, Recoveries and Fatalities in Nigeria. Sustainability. 2023; 15(9):7324. https://doi.org/10.3390/su15097324
Chicago/Turabian StyleInegbedion, Henry Egbezien. 2023. "A Time Series Forecast of COVID-19 Infections, Recoveries and Fatalities in Nigeria" Sustainability 15, no. 9: 7324. https://doi.org/10.3390/su15097324