## 4 Results
### Confidence Interval  
We also estimate the confidence interval [31] of the new proposed model for the data sets in Table 7, which is defined as:  
\[\mathrm{m(t)}\ =\mathrm{m(t)}\pm\mathrm{z}_{\alpha/2}\sqrt{\mathrm{m(t)}}, \tag{20}\]  
where \(\mathrm{z}_{\alpha/2}\) is the \(100(1-\alpha)\) percentile of the standard normal distribution. Figures 2 and 3 show the confidence interval of the proposed model for both data sets. Figures 4 and 5 show the mean value functions of all the SRGMs for both data sets. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Model** & **MSE** & **PRR** & **PP** & **R\({}^{2}\)** & **SAE** & **AIC** & **PRV** & **RMSPE** \\ \hline GO & 0.5472 & 0.1919 & 0.3174 & 0.9898 & 10.9960 & 48.9315 & 0.7004 & 0.7179 \\ \hline DS & 0.7472 & 6.2594 & 0.9673 & 0.9858 & 13.6902 & 48.5178 & 0.8226 & 0.8492 \\ \hline IS & 0.3395 & 0.0715 & 0.0605 & 0.9941 & 8.1437 & 49.3896 & 0.5489 & 0.5493 \\ \hline YID & 0.4886 & 0.1210 & 0.1786 & 0.9915 & 9.2881 & 50.5397 & 0.6564 & 0.6589 \\ \hline PNZ & 0.3621 & 0.0721 & 0.0606 & 0.9941 & 8.1484 & 51.3791 & 0.5488 & 0.5493 \\ \hline PZ & 0.3880 & 0.0722 & 0.0606 & 0.9941 & 8.1485 & 53.3790 & 0.5488 & 0.5493 \\ \hline DP2 & 5.2747 & 1.3468 & 19.3541 & 0.9135 & 32.4992 & 70.1656 & 2.0966 & 2.0966 \\ \hline TC & 0.4558 & 0.0797 & 0.0648 & 0.9930 & 8.5831 & 53.8763 & 0.5951 & 0.5954 \\ \hline New model & 0.3481 & 0.0621 & 0.0522 & 0.9951 & 7.3657 & 54.7293 & 0.5011 & 0.5014 \\ \hline \end{tabular}
\end{table} 
Table 6: Comparison of all the criteria for data set 2. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Model** & **MSE** & **PRR** & **PP** & **R\({}^{2}\)** & **SAE** & **AIC** & **PRV** & **RMSPE** \\ \hline GO & 1.6260 & 0.6277 & 0.2425 & 0.9839 & 12.9385 & 49.4088 & 1.1979 & 1.2191 \\ \hline DS & 7.3713 & 65.1778 & 1.1664 & 0.9269 & 25.6464 & 72.2377 & 2.5922 & 2.3315 \\ \hline IS & 1.7887 & 0.6279 & 0.2426 & 0.9839 & 12.9397 & 51.4089 & 1.2191 & 1.2940 \\ \hline YID & 1.7870 & 0.6278 & 0.2426 & 0.9839 & 12.9216 & 51.3945 & 1.2187 & 1.2922 \\ \hline PNZ & 2.0232 & 0.5604 & 0.2266 & 0.9836 & 12.9766 & 53.6534 & 1.2307 & 1.4418 \\ \hline PZ & 2.2359 & 0.6280 & 0.2426 & 0.9839 & 12.9400 & 55.4091 & 1.2192 & 1.6175 \\ \hline DP2 & 33.5928 & 1.0252 & 8.3639 & 0.7273 & 50.9805 & 131.6861 & 5.0194 & 5.6645 \\ \hline TC & 1.3975 & 0.0547 & 0.0696 & 0.9899 & 10.6421 & 52.2273 & 0.9640 & 1.3303 \\ \hline New model & 1.0029 & 0.0165 & 0.0152 & 0.9922 & 8.1965 & 54.1355 & 0.7760 & 0.8417 \\ \hline \end{tabular}
\end{table} 
Table 5: Comparison of all the criteria for data set 1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Data Set 1** & \multicolumn{4}{c}{**Data Set 2**} \\ \hline
**Time** & **LC** & **UC** & **Time** & **LC** & **UC** \\ \hline
1249 & 0.076714 & 7.910112 & 1 & \(-\)0.95994 & 2.962066 \\ \hline
4721 & 3.510316 & 15.64006 & 2 & \(-\)0.72276 & 5.029449 \\ \hline
8786 & 6.608054 & 21.23353 & 3 & \(-\)0.22797 & 6.968153 \\ \hline
13,669 & 9.550651 & 26.10079 & 4 & 0.413007 & 8.848266 \\ \hline
19,094 & 12.13476 & 30.16134 & 5 & 1.153972 & 10.6953 \\ \hline
24,750 & 14.27082 & 33.41065 & 6 & 1.969788 & 12.52126 \\ \hline
32,299 & 16.47781 & 36.68851 & 7 & 2.844421 & 14.33204 \\ \hline
40,594 & 18.29813 & 39.34200 & 8 & 3.766162 & 16.12977 \\ \hline
49,476 & 19.76057 & 41.44564 & 9 & 4.725129 & 17.91337 \\ \hline
55,596 & 20.55722 & 42.58206 & 10 & 5.71162 & 19.67833 \\ \hline
58,061 & 20.83969 & 42.98349 & 11 & 6.71484 & 21.41613 \\ \hline
58,588 & 20.89753 & 43.06561 & 12 & 7.721905 & 23.1137 \\ \hline
58,633 & 20.90243 & 43.07256 & 13 & 8.717243 & 24.75315 \\ \hline - & - & - & 14 & 9.682677 & 26.31238 \\ \hline - & - & - & 15 & 10.59846 & 27.76699 \\ \hline - & - & - & 16 & 11.44533 & 29.09345 \\ \hline - & - & - & 17 & 12.20722 & 30.27298 \\ \hline - & - & - & 18 & 12.87369 & 31.29499 \\ \hline - & - & - & 19 & 13.44132 & 32.15873 \\ \hline \end{tabular}
\end{table} 
Table 7: Confidence interval of the new proposed model for both data sets (\(\alpha=0.05\)).