Table 2: Some of the Principal Models in the Structural Framework
Table 2: Some of the Principal Models in the Structural Framework
| Type of model | σ 2ε | σ 2η | σ 2ξ | σ 2ω |
|---|---|---|---|---|
| Level only | ||||
| Constant mean | yes | 0 | 0 | 0 |
| Local level | yes | yes | 0 | 0 |
| Random walk | 0 | yes | 0 | 0 |
| Trend only | ||||
| Deterministic | yes | 0 | 0 | 0 |
| Local level with fixed slope | yes | yes | 0 | 0 |
| Random walk with fixed drift | 0 | yes | 0 | 0 |
| Local linear trend (Holt) | yes | yes | yes | 0 |
| Smooth trend | yes | 0 | yes | 0 |
| Second difference | 0 | 0 | yes | 0 |
| Seasonal (with selected trend) | ||||
| Fixed seasonals | (yes or 0) | (yes or 0) | (yes or 0) | 0 |
| Varying seasonals | (yes or 0) | (yes or 0) | (yes or 0) | yes |
| Basic Structural Model | yes | yes | yes | yes |
Source: Based on Koopman et al. (2000), p. 141.