Table 3.
ARIMA model selection for serious assault (Feb 2014–Feb 2020)
| Model | Description | Specification | Obs | ll(model) | df | AIC | BIC |
|---|---|---|---|---|---|---|---|
| 1 | Constant only | ARIMA(0,0,0)SARIMA(0,1,0,12) | 73 | − 162.89 | 2 | 329.77 | 334.35 |
| 2 | Seasonal differencing | ARIMA(0,0,0)SARIMA(0,1,0,12) | 73 | − 133.92 | 1 | 269.83 | 272.12 |
| 3 | Trend differencing | ARIMA(0,1,0)SARIMA(0,0,0,12) | 73 | − 123.21 | 1 | 248.43 | 250.72 |
| 4 | Seasonal and trend differencing | ARIMA(0,1,0)SARIMA(0,1,0,12) | 73 | − 118.66 | 1 | 239.33 | 241.62 |
| 5 | Model 4 with seasonal MA1 | ARIMA(0,1,0)SARIMA(0,1,1,12) | 73 | − 106.03 | 1 | 214.07 | 216.36 |
| 6 | Model 4 with seasonal AR1 | ARIMA(0,1,0)SARIMA(1,1,0,12) | 73 | − 113.10 | 2 | 230.19 | 234.78 |
| 7 | Model 4 with seasonal AR1 and MA1 | ARIMA(0,1,0)SARIMA(1,1,1,12) | 73 | − 105.90 | 3 | 217.80 | 224.67 |
| 8 | Model 5 with trend MA1 | ARIMA(0,1,1)SARIMA(0,1,1,12) | 73 | − 101.75 | 3 | 209.51 | 216.38 |
| 9 | Model 5 with trend AR1 | ARIMA(1,1,0)SARIMA(0,1,1,12) | 73 | − 105.08 | 3 | 216.16 | 223.03 |
| 10 | Model 5 with trend AR1 and MA1 | ARIMA(1,1,1)SARIMA(0,1,1,12) | 73 | − 101.65 | 4 | 211.30 | 220.47 |
The final model indicated in italic. Source: Queensland Offence rates, Open Data Portal