From c58cd4effde04620a7c1e353fe86daeb37fb65a9 Mon Sep 17 00:00:00 2001
From: andybeet <22455149+andybeet@users.noreply.github.com>
Date: Tue, 13 Aug 2024 16:47:56 -0400
Subject: [PATCH] add tags to all equations

---
 vignettes/Equations.Rmd | 9 ++++++---
 1 file changed, 6 insertions(+), 3 deletions(-)

diff --git a/vignettes/Equations.Rmd b/vignettes/Equations.Rmd
index 958fdc1..f58a267 100644
--- a/vignettes/Equations.Rmd
+++ b/vignettes/Equations.Rmd
@@ -37,7 +37,7 @@ library(arfit)
 \begin{align}
 \tag{2}
 \mathrm{L}\left( \underline{\theta}; \underline{y} \right )= \prod^n_{t=2} p\left(Y_t = y_t | Y_{t-1}=y_{t-1}\right)  p\left(Y_1=y_1 \right) 
-\end{equation}
+\end{align}
 
 ---
 
@@ -49,13 +49,15 @@ logL\left( \underline{\theta}; \underline{y} \right ) = & -\frac{n}{2}log2\pi -
 
 ---
 
-\begin{equation}
+\begin{align}
+\tag{4}
 \hat\sigma^2 = \frac{1}{n}\left( (1-\phi^2)(y_1-\beta_0-\beta_1)^2 + \sum^n_{t=2}(y_t - \phi y_{t-1}-\beta_0(1-\phi^2) - t\beta_1 + \phi(t-1)\beta_1)^2 \right) 
-\end{equation}
+\end{align}
 
 ---
 
 \begin{align}
+\tag{5}
 logL\left( \underline{\beta}, \phi; \underline{y} \right ) &= const. + \frac{1}{2}log(1-\phi^2) \notag \\
 &-\frac{n}{2}log\left( (1-\phi^2)(y_1-\beta_0-\beta_1)^2 + \sum^n_{t=2}(y_t - \phi y_{t-1}-\beta_0(1-\phi^2)-t\beta_1 + \phi(t-1)\beta_1)^2 \right) \\ 
 
@@ -66,6 +68,7 @@ logL\left( \underline{\beta}, \phi; \underline{y} \right ) &= const. + \frac{1}{
 ---
 
 \begin{align}
+\tag{6}
 logL\left( \underline{\beta}, \underline{\phi},\sigma; \underline{y} \right ) &= -\frac{n}{2}log(2\pi) -\frac{n}{2}log(\sigma^2) +\frac{1}{2}log \left|V_p^{-1} \right|
 \\
 &-\frac{1 }{2 \sigma^2} (\underline{y_p}-\underline{\mu_p})^T V_p^{-1}(\underline{y_p}-\underline{\mu_p}) \\