Testing MathJax on GitHub Pages

Inline Math

Here’s some inline math: $E = mc^2$ and $\beta < 0$. Another version with no dollar signs is \(\alpha + \beta = \gamma\).

Display Math

Display equation: \(\Delta y_t = \beta y_{t-1} + \gamma_1 \Delta y_{t-1} + \gamma_2 \Delta y_{t-2}\) or with no dollar signs: \[ \Delta y_t = \beta y_{t-1} + \gamma_1 \Delta y_{t-1} + \gamma_2 \Delta y_{t-2} \]

Aligned Equations

with dollar signs:

\[\begin{align} y_t &= \mu_t + \epsilon_t\\ \mu_{t} &= \mu_{t-1} + \delta_t \end{align}\]

and as well with no dollar signs:

\[ \begin{align} y_t &= \mu_t + \epsilon_t
\mu_{t} &= \mu_{t-1} + \delta_t \end{align} \]

Complex Expression

\[ \text{ADF} = \frac{\int W(t)dW(t)}{\bigl(\int W^2(t)dt\bigr)^{3/2}} \]

Variance Ratio

\(\text{VR} = \frac{\text{Var}(y_{t+k}-y_t)}{k \sigma^2}\)

If you can see all these equations properly formatted, MathJax is working!