Lags | SARIMA | SARIMA-GRNN | SARIMA-NARNN | SARIMA-NARNNX | ||||
Box-Ljung Q | P value | Box-Ljung Q | P value | Box-Ljung Q | P value | Box-Ljung Q | P value | |
1 | 0.079 | 0.779 | 2.287 | 0.130 | 1.769 | 0.183 | 0.057 | 0.811 |
3 | 0.084 | 0.994 | 3.308 | 0.347 | 6.010 | 0.111 | 0.336 | 0.953 |
6 | 0.970 | 0.987 | 3.969 | 0.681 | 7.375 | 0.288 | 0.436 | 0.999 |
9 | 4.065 | 0.907 | 4.850 | 0.847 | 8.940 | 0.443 | 1.348 | 0.998 |
12 | 7.396 | 0.830 | 6.097 | 0.911 | 10.706 | 0.554 | 3.160 | 0.994 |
15 | 8.480 | 0.903 | 7.667 | 0.936 | 14.006 | 0.525 | 5.059 | 0.992 |
18 | 9.763 | 0.939 | 11.351 | 0.879 | 14.478 | 0.697 | 9.189 | 0.955 |
21 | 10.959 | 0.964 | 11.446 | 0.953 | 14.997 | 0.823 | 10.320 | 0.975 |
24 | 15.399 | 0.909 | 17.626 | 0.821 | 17.174 | 0.841 | 18.569 | 0.775 |
27 | 20.056 | 0.828 | 21.015 | 0.786 | 19.064 | 0.868 | 30.082 | 0.311 |
30 | 20.803 | 0.894 | 21.071 | 0.886 | 20.029 | 0.916 | 33.156 | 0.316 |
33 | 23.485 | 0.889 | 22.172 | 0.924 | 21.507 | 0.938 | 38.354 | 0.240 |
36 | 25.866 | 0.894 | 25.066 | 0.914 | 22.383 | 0.963 | 40.113 | 0.293 |
GRNN, generalised regression neural network; NARNN, non-linear autoregressive neural network; NARNNX, non-linear autoregressive neural network with exogenous input; SARIMA, seasonal autoregressive integrated moving average.