Table 3 Forecast comparison with SARIMA.
From: Some developments on seasonal INAR processes with application to influenza data
SARIMA | INAR(1)\(_s\) ZMPL | |||||||
|---|---|---|---|---|---|---|---|---|
k | PRMSE | PMAE | PTP | PRMSE | PMAE | PTP-Mean | PTP-Med | PTP-Mode |
\(\lambda =0.3,~\alpha =0.5,~\delta =0.7\) | ||||||||
1 | 2.376 | 1.555 | 10.00 | 2.374 | 1.186 | 9.80 | 58.10 | 61.30 |
2 | 2.622 | 1.727 | 8.90 | 2.618 | 1.411 | 9.50 | 55.00 | 57.30 |
3 | 2.602 | 1.679 | 8.10 | 2.592 | 1.300 | 8.20 | 59.20 | 60.20 |
4 | 2.545 | 1.643 | 9.10 | 2.546 | 1.244 | 8.50 | 58.60 | 62.80 |
5 | 2.443 | 1.595 | 10.20 | 2.438 | 1.203 | 9.80 | 60.30 | 62.30 |
\(\lambda = 0.5,~\alpha =1,~\delta =0.5\) | ||||||||
1 | 1.787 | 1.310 | 17.50 | 1.784 | 1.140 | 17.50 | 43.10 | 47.50 |
2 | 1.671 | 1.254 | 16.60 | 1.673 | 1.035 | 16.90 | 45.20 | 51.10 |
3 | 1.791 | 1.322 | 16.10 | 1.788 | 1.122 | 16.00 | 43.30 | 50.60 |
4 | 1.809 | 1.335 | 15.30 | 1.810 | 1.134 | 15.00 | 42.30 | 49.50 |
5 | 1.834 | 1.335 | 17.00 | 1.832 | 1.128 | 17.00 | 46.00 | 48.70 |
\(\lambda = 0.6,~\alpha =1.5,~\delta =-0.5\) | ||||||||
1 | 2.391 | 1.730 | 19.60 | 2.391 | 1.701 | 19.60 | 22.20 | 23.70 |
2 | 2.209 | 1.677 | 19.00 | 2.213 | 1.645 | 18.70 | 20.70 | 22.20 |
3 | 2.483 | 1.868 | 15.60 | 2.470 | 1.839 | 15.10 | 18.00 | 21.60 |
4 | 2.307 | 1.705 | 19.50 | 2.302 | 1.674 | 18.90 | 20.80 | 22.00 |
5 | 2.300 | 1.719 | 19.50 | 2.294 | 1.683 | 19.20 | 20.90 | 22.70 |
\(\lambda = 0.7,~\alpha =2,~\delta =-1\) | ||||||||
1 | 2.584 | 1.875 | 19.20 | 2.587 | 1.858 | 18.90 | 19.90 | 20.30 |
2 | 2.448 | 1.856 | 17.30 | 2.442 | 1.841 | 17.30 | 18.10 | 20.30 |
3 | 2.586 | 1.873 | 18.90 | 2.575 | 1.849 | 18.50 | 20.50 | 22.00 |
4 | 2.565 | 1.862 | 20.90 | 2.562 | 1.846 | 20.30 | 21.10 | 19.80 |
5 | 2.752 | 1.959 | 21.30 | 2.736 | 1.953 | 21.00 | 21.60 | 20.20 |
