Alternative Equation Formats

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MathML

\begin{array}{rcl} r_{t} & = & H_{t}^{\frac{1}{2}} ϵ_{t} \\ H_{t} & = & D_{t} S_{t} D_{t} \\ D_{t} & = & [\begin{array}{cc} \sqrt{h_{11, t}} & 0 \\ 0 & \sqrt{h_{22, t}} \end{array}] \\ h_{11, t} & = & c_{11} + a_{11, 1} r_{1, t - 1}^{2} + g_{11, 1} h_{11, t - 1} \\ h_{22, t} & = & c_{11} + a_{22, 1} r_{2, t - 1}^{2} + g_{22, 1} h_{22, t - 1} \\ S_{t} & = & [\begin{array}{cc} 1 & s_{12, t} \\ s_{12, t} & 1 \end{array}] \\ s_{12, t} & = & \frac{q_{12, t}}{\sqrt{q_{11, t} q_{22, t}}} \\ q_{12, t} & = & (1 - α - β) s_{12} + α \frac{r_{1, t - 1}}{\sqrt{h_{11, t - 1}}} \frac{r_{2, t - 1}}{\sqrt{h_{22, t - 1}}} + β q_{12, t - 1} \\ q_{11, t} & = & (1 - α - β) + α \frac{r_{1, t - 1}^{2}}{h_{11, t - 1}} + β q_{11, t - 1} \\ q_{22, t} & = & (1 - α - β) + α \frac{r_{2, t - 1}^{2}}{h_{22, t - 1}} + β q_{22, t - 1} \end{array}

Math Rendered as SVG

Math as LaTeX Source

\begin{eqnarray*} r_ t & = & H_ t ^{\frac{1}{2}} \bepsilon _ t \\ H_ t & = & D_ t S_ t D_ t \\ D_ t & = & \left[ \begin{array}{cc} \sqrt{h_{11,t}} & 0 \\ 0 & \sqrt{h_{22,t}} \end{array} \right] \\ h_{11,t} & = & c_{11} + a_{11,1} r_{1,t-1}^2 + g_{11,1} h_{11,t-1} \\ h_{22,t} & = & c_{11} + a_{22,1} r_{2,t-1}^2 + g_{22,1} h_{22,t-1} \\ S_ t & = & \left[ \begin{array}{cc} 1 & s_{12,t} \\ s_{12,t} & 1 \end{array} \right] \\ s_{12,t} & = & \frac{q_{12,t}}{\sqrt{q_{11,t}q_{22,t}}} \\ q_{12,t} & = & (1-\alpha -\beta )s_{12} + \alpha \frac{r_{1,t-1}}{\sqrt{h_{11,t-1}}} \frac{r_{2,t-1}}{\sqrt{h_{22,t-1}}} + \beta q_{12,t-1} \\ q_{11,t} & = & (1-\alpha -\beta ) + \alpha \frac{r_{1,t-1}^2}{h_{11,t-1}} + \beta q_{11,t-1} \\ q_{22,t} & = & (1-\alpha -\beta ) + \alpha \frac{r_{2,t-1}^2}{h_{22,t-1}} + \beta q_{22,t-1} \end{eqnarray*}