Table 2.
Goodness-of-fit test and selection of optimal ARIMA models
| Time series | Optimal Model |
Goodness-of-fit | Ljung-Box test | ||||
|---|---|---|---|---|---|---|---|
| MASE | RMSE | AIC | BIC | χ2 | P value | ||
| AIDS incidence |
(0,1,3) × (2,0,0)12 |
0.55 | 0.03 | − 553.19 | − 535.42 | 0.00 | 0.99 |
| HIV incidence |
(3,1,0) × (1,0,1)12 |
0.69 | 0.05 | − 436.07 | − 418.29 | 0.09 | 0.77 |
| AIDS and HIV incidence |
(0,1,2) × (2,0,0)12 |
0.56 | 0.07 | − 344.62 | − 329.81 | 0.16 | 0.69 |
| AIDS death |
(0,1,3) × (1,0,0)12 |
0.62 | 0.01 | − 926.73 | − 911.92 | 0.05 | 0.83 |
| HIV death |
(0,1,3) × (1,0,0)12 |
0.61 | 0.01 | − 901.39 | − 886.58 | 0.02 | 0.89 |
|
AIDS and HIV death |
(0,1,3) × (1,0,0)12 |
0.60 | 0.02 | − 724.45 | − 709.64 | 0.03 | 0.87 |
Note: MASE Mean absolute scaled error, RMSE Root mean square error, AIC Akaike’s information criterion, BIC Bayesian information criterion