\documentclass[11pt]{article}

\usepackage{longtable,amssymb,amsmath,amsfonts}
\usepackage[dvips]{graphicx}
\addtolength{\hoffset}{-2.75cm}
\addtolength{\textwidth}{4.95cm}
\addtolength{\textheight}{2.5cm}
\addtolength{\voffset}{-2.3cm}

\newcommand{\Ukn}[1]{U_{#1,n}}
\newcommand{\Si}[1]{S_{#1}}
\newcommand{\Xs}[1]{X_{#1}}
\newcommand{\Xt}{\Xs{t}}
\newcommand{\Zs}[1]{Z_{#1}}
\newcommand{\Zt}{\Zs{t}}
%\newcommand{\Si}[1]{S(#1)}
\newcommand{\SiFrac}[1]{\frac{\Si{#1}}{\Si{n+1}}}

\begin{document}

\begin{align*}
\frac{1}{(1-r)^{n}} & = \sum_{i = 1}^{\infty}{i + n-1 \choose n-1 }r^{i}
\end{align*}
\begin{align*}
\phi(B)\Xt & = \theta(B)\Zt
\end{align*}
\begin{align*}
\Xt & = \frac{\theta(B)}{\phi(B)}\Zt = \sum_{i=0}^{\infty}\psi_{i}\Zs{t-i}
\end{align*}
\begin{align*}
\Xt & = \sum_{j=-\infty}^{\infty}\psi_{j}\Zs{t-j} \\
\gamma(k) & = \sigma^{2}\sum_{j=-\infty}^{\infty}\psi_{j}\psi_{j + |k|}
\end{align*}

\begin{align*}
\Gamma & = \{ \gamma(j - i); 1 \leq i \leq p, 1 \leq i \leq p \} \\
\gamma' & = ( \gamma(1), \gamma(2), \ldots, \gamma(p) ) \\
\phi' & = ( \phi_{1}, \ldots, \phi_{2} )
\end{align*}

Yule-Walker
\begin{align*}
\hat{\phi} & = \hat{\Gamma}'\hat{\gamma} \\
\hat{\sigma^{2}} & = \hat{\gamma}(0) - \hat{\phi}'\hat{\gamma}
\end{align*}

\end{document}
