Alternative Equation Formats

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MathML

y t N ( x t , θ 4 ) Observational model x t = μ t + s t Underlying trend after allowing for seasonal effects μ t N ( μ t 1 + α t 1 , θ 1 ) Evolution in mean α t 1 N ( ϕ α t 2 , θ 2 ) Increments in mean s t N ( s t 1 s t 2 s t 3 , θ 3 ) Seasonality

MathML rendered with MathJax

y t N ( x t , θ 4 ) Observational model x t = μ t + s t Underlying trend after allowing for seasonal effects μ t N ( μ t 1 + α t 1 , θ 1 ) Evolution in mean α t 1 N ( ϕ α t 2 , θ 2 ) Increments in mean s t N ( s t 1 s t 2 s t 3 , θ 3 ) Seasonality

Math as LaTeX Source

\begin{align*} y_ t & \sim N(x_ t,\theta _4) & \text {Observational model} \\ x_ t & = \mu _ t + s_ t & \text {Underlying trend after allowing for seasonal effects} \\ \mu _ t & \sim N(\mu _{t-1} + \alpha _{t-1}, \theta _1) & \text {Evolution in mean} \\ \alpha _{t-1} & \sim N(\phi \alpha _{t-2}, \theta _2) & \text {Increments in mean} \\ s_ t & \sim N(-s_{t-1} -s_{t-2} - s_{t-3}, \theta _3) & \text {Seasonality} \end{align*}