Alternative Equation Formats

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MathML

\begin{array}{rcl} Δ y_{t} & = & α β^{'} y_{t - 1} + Φ_{1}^{*} Δ y_{t - 1} + Θ_{0}^{*} x_{t} + ϵ_{t} \\ = & [\begin{array}{rr} 0.01 & - 0.02 \\ - 0.03 & 0.04 \\ 0.05 & - 0.06 \\ 0 & 0 \end{array}] [\begin{array}{rrrr} 1 & 0 & - 1 & 0 \\ 0 & 1 & 0 & - 1 \end{array}] y_{t - 1} \\ + [\begin{array}{rrrr} - 0.01 & 0.03 & 0.05 & - 0.02 \\ 0.02 & - 0.04 & 0.06 & 0.03 \\ 0 & 0 & 0.10 & 0 \\ 0 & 0 & 0 & 0.04 \end{array}] Δ y_{t - 1} + [\begin{array}{r} 0 \\ 0 \\ 0 \\ 0 \end{array}] x_{t} + ϵ_{t}, \\ ϵ_{t} & \sim & i i d N (0, Σ), Σ = I_{4} \end{array}

Math Rendered as SVG

Math as LaTeX Source

\begin{eqnarray*} \Delta \mb{y} _ t & =& \balpha \bbeta '\mb{y}_{t-1}+\Phi _1^*\Delta \mb{y}_{t-1} +\Theta _0^*\mb{x}_{t}+ \bepsilon _ t \\ & =& \left[ \begin{array}{rr} 0.01 & -0.02 \\ -0.03 & 0.04 \\ 0.05 & -0.06 \\ 0 & 0 \end{array} \right] \left[ \begin{array}{rrrr} 1 & 0 & -1 & 0 \\ 0 & 1 & 0 & -1 \end{array} \right] \mb{y}_{t-1} \\ & & + \left[ \begin{array}{rrrr} -0.01 & 0.03 & 0.05 & -0.02 \\ 0.02 & -0.04 & 0.06 & 0.03 \\ 0 & 0 & 0.10 & 0 \\ 0 & 0 & 0 & 0.04 \end{array} \right] \Delta \mb{y}_{t-1} + \left[ \begin{array}{r} 0 \\ 0 \\ 0 \\ 0 \end{array} \right] \mb{x}_{t} + \bepsilon _ t, \\ \bepsilon _ t & \sim & \mr{iid}~ N(0,\Sigma ),\Sigma =I_4 \end{eqnarray*}