Table 2. Benchmarking of p and q lag orders, implementation time, and the value of GOF statistic for the full-search and the proposed algorithm for Trials 1, 2, 4, and 5.
| Trial | Full-Search algorithm | Proposed algorithm | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Statistic | p | q | Time (sec) |
Value | p | q | Time (sec) |
Value | |||
| X1 | X2 | X1 | X2 | ||||||||
| 1 | AIC | 1 | 1 | 1 | 3.96 | -247.3 | 1 | 1 | 1 | 1.64 | -247.3 |
| BIC | 1 | 1 | 1 | 3.67 | -255.8 | 1 | 1 | 1 | 1.66 | -255.8 | |
| MASE | 5 | 5 | 5 | 3.65 | 0.337 | 4 | 3 | 5 | 1.80 | 0.340 | |
| GMRAE | 4 | 3 | 5 | 3.59 | 0.239 | 4 | 3 | 5 | 1.79 | 0.239 | |
| 2 | AIC | 4 | 4 | 4 | 13.01 | -727.6 | 4 | 3 | 4 | 3.13 | -725.6 |
| BIC | 4 | 1 | 4 | 12.67 | -677.1 | 4 | 1 | 4 | 4.71 | -677.1 | |
| MASE | 5 | 7 | 7 | 13.07 | 0.124 | 5 | 7 | 7 | 4.66 | 0.124 | |
| GMRAE | 5 | 6 | 6 | 13.27 | 0.080 | 4 | 7 | 4 | 4.63 | 0.084 | |
| 4 | AIC | 2 | 2 | 10 | 143.6 | 6413 | 1 | 1 | 10 | 15.69 | 6413 |
| BIC | 1 | 1 | 10 | 140.2 | 6515 | 1 | 1 | 10 | 29.83 | 6515 | |
| MASE | 8 | 9 | 9 | 136.6 | 0.514 | 8 | 9 | 9 | 26.69 | 0.514 | |
| GMRAE | 4 | 8 | 8 | 137.9 | 0.509 | 5 | 3 | 8 | 17.01 | 0.512 | |
| 5 | AIC | 5 | 4 | 5 | 35.81 | 40397 | 5 | 4 | 5 | 13.87 | 40397 |
| BIC | 1 | 3 | 5 | 35.43 | 40509 | 1 | 3 | 5 | 13.62 | 40509 | |
| MASE | 5 | 4 | 5 | 34.27 | 0.435 | 5 | 4 | 5 | 13.15 | 0.435 | |
| GMRAE | 4 | 2 | 5 | 33.85 | 0.565 | 4 | 2 | 5 | 10.73 | 0.565 | |