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Table 2: Some of the Principal Models in the Structural Framework

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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.
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