Forecast lag for 35 days


Call:
lm(formula = Case ~ splines::bs(Day, knots = NULL), data = Data)

Residuals:
    Min      1Q  Median      3Q     Max 
-512.75 -157.78  -28.01  125.63 2119.04 

Coefficients:
                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                      -406.18      49.59  -8.191 6.36e-15 ***
splines::bs(Day, knots = NULL)1  2275.34     143.37  15.871  < 2e-16 ***
splines::bs(Day, knots = NULL)2 -1001.06      91.20 -10.977  < 2e-16 ***
splines::bs(Day, knots = NULL)3  1718.97      78.22  21.976  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 225 on 318 degrees of freedom
Multiple R-squared:  0.6115,    Adjusted R-squared:  0.6079 
F-statistic: 166.9 on 3 and 318 DF,  p-value: < 2.2e-16


Call:
lm(formula = Case ~ splines::bs(Day, knots = BREAKS), data = Data)

Residuals:
    Min      1Q  Median      3Q     Max 
-604.76  -55.96   -0.92   35.73 2176.63 

Coefficients:
                                   Estimate Std. Error t value Pr(>|t|)    
(Intercept)                          0.5665    66.6249   0.009   0.9932    
splines::bs(Day, knots = BREAKS)1   -9.1875   128.9091  -0.071   0.9432    
splines::bs(Day, knots = BREAKS)2   26.9559    83.6282   0.322   0.7474    
splines::bs(Day, knots = BREAKS)3  819.4142    96.2080   8.517 6.97e-16 ***
splines::bs(Day, knots = BREAKS)4  202.3050    82.4064   2.455   0.0146 *  
splines::bs(Day, knots = BREAKS)5  124.9019    94.9009   1.316   0.1891    
splines::bs(Day, knots = BREAKS)6   66.6177   100.3576   0.664   0.5073    
splines::bs(Day, knots = BREAKS)7 1066.7423   109.6299   9.730  < 2e-16 ***
splines::bs(Day, knots = BREAKS)8 1512.0313   101.5294  14.893  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 174.6 on 313 degrees of freedom
Multiple R-squared:  0.7699,    Adjusted R-squared:  0.764 
F-statistic: 130.9 on 8 and 313 DF,  p-value: < 2.2e-16

           Length Class             Mode   
x          322    -none-            numeric
y          322    -none-            numeric
w          322    -none-            numeric
yin        322    -none-            numeric
tol          1    -none-            numeric
data         3    -none-            list   
no.weights   1    -none-            logical
lev        322    -none-            numeric
cv.crit      1    -none-            numeric
pen.crit     1    -none-            numeric
crit         1    -none-            numeric
df           1    -none-            numeric
spar         1    -none-            numeric
ratio        1    -none-            numeric
lambda       1    -none-            numeric
iparms       5    -none-            numeric
auxM         0    -none-            NULL   
fit          5    smooth.spline.fit list   
call         3    -none-            call

Series: Data$Case 
ARIMA(3,1,2) with drift 

Coefficients:
         ar1      ar2      ar3      ma1     ma2   drift
      0.7027  -0.3099  -0.1572  -1.2158  0.4589  4.7247
s.e.  0.1581   0.0855   0.0773   0.1521  0.1226  3.0837

sigma^2 estimated as 30437:  log likelihood=-2109.81
AIC=4233.61   AICc=4233.97   BIC=4260.01

Training set error measures:
                      ME     RMSE      MAE  MPE MAPE      MASE         ACF1
Training set -0.04542223 172.5554 87.15863 -Inf  Inf 0.9026301 -0.006942934


Call:
stats::lm(formula = Case ~ Day + I(Day^2), data = Data)

Residuals:
    Min      1Q  Median      3Q     Max 
-497.89 -211.00  -82.38  197.42 2127.72 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)   
(Intercept) 166.139409  53.054623   3.131  0.00190 **
Day          -0.299900   0.758519  -0.395  0.69283   
I(Day^2)      0.006473   0.002274   2.846  0.00471 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 315.4 on 319 degrees of freedom
Multiple R-squared:  0.2347,    Adjusted R-squared:  0.2299 
F-statistic: 48.92 on 2 and 319 DF,  p-value: < 2.2e-16

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 -47.74  204.87  281.75  342.49  455.65 1321.24


Call:
lm(formula = Data$Day ~ Without.knots * With.knots * Smooth * 
    Quadratic * ARIMA)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.88791 -0.31733  0.01936  0.33268  2.07747 

Coefficients:
                                                  Estimate Std. Error t value
(Intercept)                                     -1.068e+02  1.657e+00 -64.455
Without.knots                                    1.651e-01  5.652e-03  29.219
With.knots                                       4.885e-01  2.546e-02  19.190
Smooth                                          -2.828e-02  4.789e-02  -0.591
Quadratic                                        7.540e-01  9.010e-03  83.680
ARIMA                                            3.437e-01  2.796e-02  12.291
Without.knots:With.knots                        -7.839e-04  7.080e-05 -11.073
Without.knots:Smooth                            -2.954e-05  1.504e-04  -0.196
With.knots:Smooth                               -7.174e-04  6.350e-05 -11.297
Without.knots:Quadratic                         -7.309e-04  3.273e-05 -22.329
With.knots:Quadratic                            -3.056e-04  5.459e-05  -5.598
Smooth:Quadratic                                 1.603e-04  1.177e-04   1.362
Without.knots:ARIMA                             -9.442e-04  8.217e-05 -11.490
With.knots:ARIMA                                -6.319e-04  8.240e-05  -7.669
Smooth:ARIMA                                     6.351e-05  2.123e-04   0.299
Quadratic:ARIMA                                 -7.520e-04  7.340e-05 -10.245
Without.knots:With.knots:Smooth                  1.379e-06  1.339e-07  10.301
Without.knots:With.knots:Quadratic               9.608e-07  1.153e-07   8.335
Without.knots:Smooth:Quadratic                  -1.124e-07  3.955e-07  -0.284
With.knots:Smooth:Quadratic                      7.976e-07  1.695e-07   4.705
Without.knots:With.knots:ARIMA                   1.624e-06  2.164e-07   7.508
Without.knots:Smooth:ARIMA                       4.478e-07  5.458e-07   0.820
With.knots:Smooth:ARIMA                          5.955e-07  9.242e-08   6.444
Without.knots:Quadratic:ARIMA                    2.607e-06  2.416e-07  10.792
With.knots:Quadratic:ARIMA                      -8.092e-08  2.016e-07  -0.401
Smooth:Quadratic:ARIMA                           2.606e-08  5.906e-07   0.044
Without.knots:With.knots:Smooth:Quadratic       -1.655e-09  1.673e-10  -9.891
Without.knots:With.knots:Smooth:ARIMA           -1.999e-09  2.177e-10  -9.183
Without.knots:With.knots:Quadratic:ARIMA        -2.170e-09  3.159e-10  -6.870
Without.knots:Smooth:Quadratic:ARIMA            -1.682e-09  1.633e-09  -1.030
With.knots:Smooth:Quadratic:ARIMA                2.926e-10  3.959e-10   0.739
Without.knots:With.knots:Smooth:Quadratic:ARIMA  2.497e-12  4.286e-13   5.826
                                                Pr(>|t|)    
(Intercept)                                      < 2e-16 ***
Without.knots                                    < 2e-16 ***
With.knots                                       < 2e-16 ***
Smooth                                             0.555    
Quadratic                                        < 2e-16 ***
ARIMA                                            < 2e-16 ***
Without.knots:With.knots                         < 2e-16 ***
Without.knots:Smooth                               0.844    
With.knots:Smooth                                < 2e-16 ***
Without.knots:Quadratic                          < 2e-16 ***
With.knots:Quadratic                            5.03e-08 ***
Smooth:Quadratic                                   0.174    
Without.knots:ARIMA                              < 2e-16 ***
With.knots:ARIMA                                2.65e-13 ***
Smooth:ARIMA                                       0.765    
Quadratic:ARIMA                                  < 2e-16 ***
Without.knots:With.knots:Smooth                  < 2e-16 ***
Without.knots:With.knots:Quadratic              3.15e-15 ***
Without.knots:Smooth:Quadratic                     0.777    
With.knots:Smooth:Quadratic                     3.94e-06 ***
Without.knots:With.knots:ARIMA                  7.46e-13 ***
Without.knots:Smooth:ARIMA                         0.413    
With.knots:Smooth:ARIMA                         4.84e-10 ***
Without.knots:Quadratic:ARIMA                    < 2e-16 ***
With.knots:Quadratic:ARIMA                         0.688    
Smooth:Quadratic:ARIMA                             0.965    
Without.knots:With.knots:Smooth:Quadratic        < 2e-16 ***
Without.knots:With.knots:Smooth:ARIMA            < 2e-16 ***
Without.knots:With.knots:Quadratic:ARIMA        3.93e-11 ***
Without.knots:Smooth:Quadratic:ARIMA               0.304    
With.knots:Smooth:Quadratic:ARIMA                  0.461    
Without.knots:With.knots:Smooth:Quadratic:ARIMA 1.50e-08 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.6401 on 290 degrees of freedom
Multiple R-squared:      1, Adjusted R-squared:      1 
F-statistic: 2.19e+05 on 31 and 290 DF,  p-value: < 2.2e-16


Call:
lm(formula = Data$Day ~ Without.knots + With.knots + Smooth + 
    Quadratic + ARIMA)

Residuals:
    Min      1Q  Median      3Q     Max 
-65.721 -18.620   6.591  22.907  32.071 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)   -16.225692   3.329593  -4.873 1.74e-06 ***
Without.knots   0.005861   0.012435   0.471  0.63774    
With.knots      0.001286   0.030317   0.042  0.96620    
Smooth         -0.063431   0.033782  -1.878  0.06135 .  
Quadratic       0.514149   0.010835  47.453  < 2e-16 ***
ARIMA           0.061062   0.017414   3.507  0.00052 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 26.49 on 316 degrees of freedom
Multiple R-squared:  0.9203,    Adjusted R-squared:  0.919 
F-statistic: 729.6 on 5 and 316 DF,  p-value: < 2.2e-16

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 -31.77  197.30  254.54  293.72  366.25 1061.51

Model	Case
Without knots	1735610
Smooth Spline	1938601
With knots	2631001
Quadratic Polynomial	439392
Lower ARIMA	296126
Upper ARIMA	1166921
Ensembled with equal weight	1652569
Ensembled based on weight	155723
Ensembled based on summed weight	212240
Ensembled based on weight of fit	1269929

Models	RMSE
Without knots	223.64
Smooth Spline	172.13
With knots	157.04
Quadratic Polynomial	313.9
Lower ARIMA	172.56
Upper ARIMA	172.56
Ensembled with equal weight	179.41
Ensembled based on weight	373.09
Ensembled based on summed weight	371.95
Ensembled based on weight of fit	204.9

Forecast lag for 28 days

Model	Case
Without knots	2057292
Smooth Spline	1620443
With knots	1369337
Quadratic Polynomial	607863
Lower ARIMA	299518
Upper ARIMA	1196662
Ensembled with equal weight	1656812
Ensembled based on weight	162663
Ensembled based on summed weight	243859
Ensembled based on weight of fit	1296835

Models	RMSE
Without knots	223.65
Smooth Spline	172.81
With knots	158.19
Quadratic Polynomial	328.78
Lower ARIMA	171.66
Upper ARIMA	171.66
Ensembled with equal weight	180.45
Ensembled based on weight	410.54
Ensembled based on summed weight	408.61
Ensembled based on weight of fit	240.7

Forecast lag for 21 days


Call:
lm(formula = Data$Day ~ Without.knots + With.knots + Smooth + 
    Quadratic + ARIMA)

Residuals:
    Min      1Q  Median      3Q     Max 
-117.66  -25.91   15.71   34.98   45.76 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)   37.778850   4.248295   8.893   <2e-16 ***
Without.knots  0.001310   0.019087   0.069    0.945    
With.knots     0.005022   0.052131   0.096    0.923    
Smooth        -0.050231   0.058718  -0.855    0.393    
Quadratic      0.334519   0.013120  25.497   <2e-16 ***
ARIMA          0.044683   0.027991   1.596    0.111    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 43.15 on 330 degrees of freedom
Multiple R-squared:  0.8057,    Adjusted R-squared:  0.8027 
F-statistic: 273.6 on 5 and 330 DF,  p-value: < 2.2e-16

Model	Case
Without knots	2277917
Smooth Spline	516803
With knots	-424438
Quadratic Polynomial	750836
Lower ARIMA	-22084
Upper ARIMA	970947
Ensembled with equal weight	1190672
Ensembled based on weight	168092
Ensembled based on summed weight	274060
Ensembled based on weight of fit	990701

Models	RMSE
Without knots	234.88
Smooth Spline	186.92
With knots	173.68
Quadratic Polynomial	342
Lower ARIMA	193.39
Upper ARIMA	193.39
Ensembled with equal weight	196.09
Ensembled based on weight	446.17
Ensembled based on summed weight	444.14
Ensembled based on weight of fit	268.77

Forecast lag for 14 days

Model	Case
Without knots	2337238
Smooth Spline	-940016
With knots	-290072
Quadratic Polynomial	839718
Lower ARIMA	-82525
Upper ARIMA	976605
Ensembled with equal weight	429533
Ensembled based on weight	175131
Ensembled based on summed weight	258126
Ensembled based on weight of fit	374609

Models	RMSE
Without knots	249.36
Smooth Spline	196.79
With knots	183.89
Quadratic Polynomial	345.19
Lower ARIMA	207.52
Upper ARIMA	207.52
Ensembled with equal weight	207.51
Ensembled based on weight	465.95
Ensembled based on summed weight	463.91
Ensembled based on weight of fit	285.16

Forecast lag for 07 days

Model	Case
Without knots	2216268
Smooth Spline	-2739209
With knots	-1731296
Quadratic Polynomial	863812
Lower ARIMA	-299110
Upper ARIMA	941280
Ensembled with equal weight	329698
Ensembled based on weight	121185
Ensembled based on summed weight	285206
Ensembled based on weight of fit	-203787

Models	RMSE
Without knots	273.66
Smooth Spline	201.11
With knots	189.36
Quadratic Polynomial	345.69
Lower ARIMA	210.02
Upper ARIMA	210.02
Ensembled with equal weight	214.27
Ensembled based on weight	472.14
Ensembled based on summed weight	470.11
Ensembled based on weight of fit	289.68

Forecast lag for 04 days

Model	Case
Without knots	2123801
Smooth Spline	-3430750
With knots	81877
Quadratic Polynomial	858682
Lower ARIMA	-333791
Upper ARIMA	893482
Ensembled with equal weight	251289
Ensembled based on weight	182705
Ensembled based on summed weight	284537
Ensembled based on weight of fit	-245137

Models	RMSE
Without knots	285.86
Smooth Spline	201.39
With knots	146.49
Quadratic Polynomial	346.64
Lower ARIMA	212.55
Upper ARIMA	212.55
Ensembled with equal weight	206.12
Ensembled based on weight	472.55
Ensembled based on summed weight	470.57
Ensembled based on weight of fit	283.83

Forecast lag for 03 days

Model	Case
Without knots	2137588
Smooth Spline	-3255146
With knots	-975910
Quadratic Polynomial	872117
Lower ARIMA	-257655
Upper ARIMA	932579
Ensembled with equal weight	281141
Ensembled based on weight	126213
Ensembled based on summed weight	294218
Ensembled based on weight of fit	-439617

Models	RMSE
Without knots	285.95
Smooth Spline	203.9
With knots	191.7
Quadratic Polynomial	346.32
Lower ARIMA	213.85
Upper ARIMA	213.85
Ensembled with equal weight	218.68
Ensembled based on weight	474.97
Ensembled based on summed weight	473.02
Ensembled based on weight of fit	289.41

Forecast lag for 02 days

Model	Case
Without knots	2127462
Smooth Spline	-3267667
With knots	-486364
Quadratic Polynomial	877445
Lower ARIMA	-255679
Upper ARIMA	936630
Ensembled with equal weight	350767
Ensembled based on weight	136752
Ensembled based on summed weight	288956
Ensembled based on weight of fit	197863

Models	RMSE
Without knots	287.39
Smooth Spline	204.36
With knots	191.21
Quadratic Polynomial	345.87
Lower ARIMA	213.55
Upper ARIMA	213.55
Ensembled with equal weight	218.77
Ensembled based on weight	475.83
Ensembled based on summed weight	473.89
Ensembled based on weight of fit	290.21

Forecast lag for 01 day

Model	Case
Without knots	2102598
Smooth Spline	-3387905
With knots	345123
Quadratic Polynomial	877424
Lower ARIMA	-263090
Upper ARIMA	933173
Ensembled with equal weight	346386
Ensembled based on weight	187664
Ensembled based on summed weight	285674
Ensembled based on weight of fit	161969

Models	RMSE
Without knots	290.12
Smooth Spline	204.25
With knots	149.6
Quadratic Polynomial	345.75
Lower ARIMA	213.27
Upper ARIMA	213.27
Ensembled with equal weight	208.16
Ensembled based on weight	475.93
Ensembled based on summed weight	474.04
Ensembled based on weight of fit	286.56

Combined Forecast

Model	Jan 16, 21 - Dec 03, 21	Jan 23, 21 - Dec 17, 21	Feb 06, 21 - Jan 14, 22	Feb 13, 21 - Jan 28, 22	Feb 16, 21 - Feb 03, 22	Feb 17, 21 - Feb 05, 22	Feb 18, 21 - Feb 07, 22	Feb 19, 21 - Feb 09, 22
Without knots	1735610	2057292	2337238	2216268	2123801	2137588	2127462	2102598
Smooth Spline	1938601	1620443	-940016	-2739209	-3430750	-3255146	-3267667	-3387905
With knots	2631001	1369337	-290072	-1731296	81877	-975910	-486364	345123
Quadratic Polynomial	439392	607863	839718	863812	858682	872117	877445	877424
Lower ARIMA	296126	299518	-82525	-299110	-333791	-257655	-255679	-263090
Upper ARIMA	1166921	1196662	976605	941280	893482	932579	936630	933173
Essembled with equal weight	1652569	1656812	429533	329698	251289	281141	350767	346386
Essembled based on weight	155723	162663	175131	121185	182705	126213	136752	187664
Essembled based on summed weight	212240	243859	258126	285206	284537	294218	288956	285674
Essembled based on weight of fit	1269929	1296835	374609	-203787	-245137	-439617	197863	161969

Combined RMSE

Model	Jan 16, 21 - Dec 03, 21	Jan 23, 21 - Dec 17, 21	Feb 06, 21 - Jan 14, 22	Feb 13, 21 - Jan 28, 22	Feb 16, 21 - Feb 03, 22	Feb 17, 21 - Feb 05, 22	Feb 18, 21 - Feb 07, 22	Feb 19, 21 - Feb 09, 22
Without knots	223.64	223.65	249.36	273.66	285.86	285.95	287.39	290.12
Smooth Spline	172.13	172.81	196.79	201.11	201.39	203.9	204.36	204.25
With knots	157.04	158.19	183.89	189.36	146.49	191.7	191.21	149.6
Quadratic Polynomial	313.9	328.78	345.19	345.69	346.64	346.32	345.87	345.75
Lower ARIMA	172.56	171.66	207.52	210.02	212.55	213.85	213.55	213.27
Upper ARIMA	172.56	171.66	207.52	210.02	212.55	213.85	213.55	213.27
Essembled with equal weight	179.41	180.45	207.51	214.27	206.12	218.68	218.77	208.16
Essembled based on weight	373.09	410.54	465.95	472.14	472.55	474.97	475.83	475.93
Essembled based on summed weight	371.95	408.61	463.91	470.11	470.57	473.02	473.89	474.04
Essembled based on weight of fit	204.9	240.7	285.16	289.68	283.83	289.41	290.21	286.56

Time varying forecast of confirmed COVID-19 cases in Nigeia

Job Nmadu

2/11/2021

Forecast lag for 35 days

Forecast lag for 28 days

Forecast lag for 21 days

Forecast lag for 14 days

Forecast lag for 07 days

Forecast lag for 04 days

Forecast lag for 03 days

Forecast lag for 02 days

Forecast lag for 01 day

Combined Forecast

Combined RMSE

Combined plots