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

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 Type of model Level only Trend only Seasonal (with selected trend) σ 2ε σ 2η σ 2ξ σ 2ω Constant mean yes 0 0 0 Local level yes yes 0 0 Random walk 0 yes 0 0 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 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.

Updated: Saturday, May 20, 2017