\documentclass[11pt]{article}

\usepackage{longtable,amssymb,amsmath,amsfonts}
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\newcommand{\Xt}{X_{t}}

\begin{document}

\begin{enumerate}
\item $\Xt = \rho X_{t-1} + \varepsilon_{t}$, $-\infty < t < \infty$, $|\rho| < 1$, $\varepsilon_{t} \sim iid$, $E\varepsilon_{t} = 0$, $E\varepsilon_{t} = \sigma^{2}$.
	\begin{enumerate}
	\item find an estimator for $\sigma^{2}$.


	\end{enumerate}
\item Let $\Xt = \varphi_{1}X_{t-1} + \varphi_{2}X_{t-2} + \varepsilon_{t}$, $1 \leq t \leq n$.
	\begin{enumerate}
	\item find the least squares estimates for $\varphi_{1}$ and $\varphi_{2}$.

	We need to minimize
	\begin{align*}
	\sum_{t=1}^{n}(X_{t} - \varphi_{1}X_{t-1} - \varphi_{2}X_{t-2})^{2}
	\end{align*}

	\end{enumerate}
\end{enumerate}

\end{document}
