%\VignetteIndexEntry{The rmgarch models: Background and properties}
%\VignetteDepends{parallel}
%\VignetteKeywords{GARCH}
%\VignettePackage{rmgarch}
\documentclass[11pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{appendix}
\usepackage[round]{natbib}
\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{anysize}
\usepackage{amsfonts}
\usepackage{courier}
\usepackage{lscape}
\usepackage{ctable}
\usepackage{subfig}
\usepackage{etex}
\usepackage[active]{srcltx}
\usepackage[]{latexsym}
\usepackage{inputenc}
\usepackage{pifont}
\usepackage{lmodern}
\usepackage[normalem]{ulem}
\usepackage{hyperref}
\marginsize{2cm}{2cm}{1cm}{1cm}
\setlength{\textwidth}{16cm}
\setlength{\oddsidemargin}{0cm}
\setlength{\textheight}{24cm}
\setlength{\headheight}{2cm}
\newtheorem{proof}{Proof}
\usepackage{Sweave}
\newtheorem{defn}{Definition}
\newtheorem{property}{Property}
\newcommand{\mbSigma}{\ensuremath{\mbox{\boldmath$\Sigma$}}}
\newcommand{\smbSigma}{\ensuremath{\mbox{\boldmath$\scriptstyle \Sigma$}}}
\newcommand{\mbLambda}{\ensuremath{\mbox{\boldmath$\Lambda$}}}
\newcommand{\mbUpsilon}{\ensuremath{\mbox{\boldmath$\Upsilon$}}}
\newcommand{\mbOmega}{\ensuremath{\mbox{\boldmath$\Omega$}}}
\newcommand{\smbOmega}{\ensuremath{\mbox{\boldmath$\scriptstyle \Omega$}}}
\newcommand{\mbPhi}{\ensuremath{\mbox{\boldmath$\Phi$}}}
\newcommand{\mbPsi}{\ensuremath{\mbox{\boldmath$\Psi$}}}
\newcommand{\mbGamma}{\ensuremath{\mbox{\boldmath$\Gamma$}}}
\newcommand{\mbPi}{\ensuremath{\mbox{\boldmath$\Pi$}}}
\newcommand{\mbTheta}{\ensuremath{\mbox{\boldmath$\Theta$}}}
\newcommand{\mbXi}{\ensuremath{\mbox{\boldmath$\Xi$}}}
\newcommand{\smbTheta}{\ensuremath{\mbox{\boldmath$\scriptstyle \Theta$}}}
\newcommand{\smbXi}{\ensuremath{\mbox{\boldmath$\scriptstyle \Xi$}}}
\newcommand{\bftheta}{\ensuremath{\mbox{\boldmath$\theta$}}}
\newcommand{\wbftheta}{\ensuremath{\mbox{\boldmath$\widehat{\theta}$}}}
\newcommand{\sbftheta}{\ensuremath{\mbox{\boldmath$\scriptstyle \theta$}}}
\newcommand{\swbftheta}{\ensuremath{\mbox{\boldmath$\scriptstyle \widehat{\theta}$}}}
\newcommand{\bfmu}{\ensuremath{\mbox{\boldmath$\mu$}}}
\newcommand{\sbfmu}{\ensuremath{\mbox{\boldmath$\scriptstyle \mu$}}}
\newcommand{\bfiota}{\ensuremath{\mbox{\boldmath$\iota$}}}
\newcommand{\sbfiota}{\ensuremath{\mbox{\boldmath$\scriptstyle \iota$}}}
\newcommand{\bfpsi}{\ensuremath{\mbox{\boldmath$\psi$}}}
\newcommand{\sbfpsi}{\ensuremath{\mbox{\boldmath$\scriptstyle \psi$}}}
\newcommand{\bfphi}{\ensuremath{\mbox{\boldmath$\phi$}}}
\newcommand{\sbfphi}{\ensuremath{\mbox{\boldmath$\scriptstyle \phi$}}}
\newcommand{\bfkappa}{\ensuremath{\mbox{\boldmath$\kappa$}}}
\newcommand{\bfvarphi}{\ensuremath{\mbox{\boldmath$\varphi$}}}
\newcommand{\sbfvarphi}{\ensuremath{\mbox{\boldmath$\scriptstyle \varphi$}}}
\newcommand{\bfnu}{\ensuremath{\mbox{\boldmath$\nu$}}}
\newcommand{\sbfnu}{\ensuremath{\mbox{\boldmath$\scriptstyle \nu$}}}
\newcommand{\bfpi}{\ensuremath{\mbox{\boldmath$\pi$}}}
\newcommand{\sbfpi}{\ensuremath{\mbox{\boldmath$\scriptstyle \pi$}}}
\newcommand{\bfepsilon}{\ensuremath{\mbox{\boldmath$\epsilon$}}}
\newcommand{\bfvarepsilon}{\ensuremath{\mbox{\boldmath$\varepsilon$}}}
\newcommand{\bfbeta}{\ensuremath{\mbox{\boldmath$\beta$}}}
\newcommand{\sbfbeta}{\ensuremath{\mbox{\boldmath$\scriptstyle \beta$}}}
\newcommand{\bfeta}{\ensuremath{\mbox{\boldmath$\eta$}}}
\newcommand{\sbfeta}{\ensuremath{\mbox{\boldmath$\scriptstyle \eta$}}}
\newcommand{\swbfbeta}{\ensuremath{\mbox{\boldmath$\scriptstyle \widehat{\beta}$}}}
\newcommand{\wbfbeta}{\ensuremath{\widehat{\mbox{\boldmath$\beta$}}}}
\newcommand{\bfgamma}{\ensuremath{\mbox{\boldmath$\gamma$}}}
\newcommand{\sbfgamma}{\ensuremath{\mbox{\boldmath$\scriptstyle \gamma$}}}
\newcommand{\bfdelta}{\ensuremath{\mbox{\boldmath$\delta$}}}
\newcommand{\bflambda}{\ensuremath{\mbox{\boldmath$\lambda$}}}
\newcommand{\sbflambda}{\ensuremath{\mbox{\boldmath$\scriptstyle \lambda$}}}
\newcommand{\bfzeta}{\ensuremath{\mbox{\boldmath$\zeta$}}}
\newcommand{\bfalpha}{\ensuremath{\mbox{\boldmath$\alpha$}}}
\newcommand{\sbfalpha}{\ensuremath{\mbox{\boldmath$\scriptstyle \alpha$}}}
\newcommand{\bfsigma}{\ensuremath{\mbox{\boldmath$\sigma$}}}
\newcommand{\bfomega}{\ensuremath{\mbox{\boldmath$\omega$}}}
\newcommand{\sbfomega}{\ensuremath{\mbox{\boldmath$\scriptstyle \omega$}}}
\newcommand{\bftau}{\ensuremath{\mbox{\boldmath$\tau$}}}
\newcommand{\bfxi}{\ensuremath{\mbox{\boldmath$\xi$}}}
\newcommand{\wsigma}{\ensuremath{\widehat{\sigma}}}
\newcommand{\bfx}{\ensuremath{\mbox{\boldmath$x$}}}
\newcommand{\sbfx}{\ensuremath{\mbox{\boldmath$\scriptstyle x$}}}
\newcommand{\bfp}{\ensuremath{\mbox{\boldmath$p$}}}
\newcommand{\bfq}{\ensuremath{\mbox{\boldmath$q$}}}
\newcommand{\bfy}{\ensuremath{\mbox{\boldmath$y$}}}
\newcommand{\wbfy}{\ensuremath{\widehat{\mbox{\boldmath$y$}}}}
\newcommand{\bfz}{\ensuremath{\mbox{\boldmath$z$}}}
\newcommand{\sbfz}{\ensuremath{\mbox{\boldmath$\scriptstyle z$}}}
\newcommand{\bfu}{\ensuremath{\mbox{\boldmath$u$}}}
\newcommand{\wbfu}{\ensuremath{\widehat{\mbox{\boldmath$u$}}}}
\newcommand{\bfw}{\ensuremath{\mbox{\boldmath$w$}}}
\newcommand{\sbfw}{\ensuremath{\mbox{\boldmath$\scriptstyle w$}}}
\newcommand{\bfr}{\ensuremath{\mbox{\boldmath$r$}}}
\newcommand{\bfh}{\ensuremath{\mbox{\boldmath$h$}}}
\newcommand{\sbfr}{\ensuremath{\mbox{\boldmath$\scriptstyle r$}}}
\newcommand{\sbfp}{\ensuremath{\mbox{\boldmath$\scriptstyle p$}}}
\newcommand{\bfs}{\ensuremath{\mbox{\boldmath$s$}}}
\newcommand{\sbfs}{\ensuremath{\mbox{\boldmath$\scriptstyle s$}}}
\newcommand{\bfe}{\ensuremath{\mbox{\boldmath$e$}}}
\newcommand{\sbfe}{\ensuremath{\mbox{\boldmath$\scriptstyle e$}}}
\newcommand{\bff}{\ensuremath{\mbox{\boldmath$f$}}}
\newcommand{\bfg}{\ensuremath{\mbox{\boldmath$g$}}}
\newcommand{\bfj}{\ensuremath{\mbox{\boldmath$j$}}}
\newcommand{\bfk}{\ensuremath{\mbox{\boldmath$k$}}}
\newcommand{\sbff}{\ensuremath{\mbox{\boldmath$\scriptstyle f$}}}
\newcommand{\bfa}{\ensuremath{\mbox{\boldmath$a$}}}
\newcommand{\sbfa}{\ensuremath{\mbox{\boldmath$\scriptstyle a$}}}
\newcommand{\bfb}{\ensuremath{\mbox{\boldmath$b$}}}
\newcommand{\bfc}{\ensuremath{\mbox{\boldmath$c$}}}
\newcommand{\bfm}{\ensuremath{\mbox{\boldmath$m$}}}
\newcommand{\sbfm}{\ensuremath{\mbox{\boldmath$\scriptstyle m$}}}
\newcommand{\bfv}{\ensuremath{\mbox{\boldmath$v$}}}
\newcommand{\sbfv}{\ensuremath{\mbox{\boldmath$\scriptstyle v$}}}
\newcommand{\bft}{\ensuremath{\mbox{\boldmath$t$}}}
\newcommand{\sbft}{\ensuremath{\mbox{\boldmath$\scriptstyle t$}}}
\newcommand{\bfzero}{\textbf{0}}
\newcommand{\bfd}{\ensuremath{\mbox{\boldmath$d$}}}
\newcommand{\bfA}{\ensuremath{\mbox{\boldmath$A$}}}
\newcommand{\bfB}{\ensuremath{\mbox{\boldmath$B$}}}
\newcommand{\bfC}{\ensuremath{\mbox{\boldmath$C$}}}
\newcommand{\bfD}{\ensuremath{\mbox{\boldmath$D$}}}
\newcommand{\bfE}{\ensuremath{\mbox{\boldmath$E$}}}
\newcommand{\bfF}{\ensuremath{\mbox{\boldmath$F$}}}
\newcommand{\bfG}{\ensuremath{\mbox{\boldmath$G$}}}
\newcommand{\bfH}{\ensuremath{\mbox{\boldmath$H$}}}
\newcommand{\bfK}{\ensuremath{\mbox{\boldmath$K$}}}
\newcommand{\bfJ}{\ensuremath{\mbox{\boldmath$J$}}}
\newcommand{\bfI}{\ensuremath{\mbox{\boldmath$I$}}}
\newcommand{\bfL}{\ensuremath{\mbox{\boldmath$L$}}}
\newcommand{\bfM}{\ensuremath{\mbox{\boldmath$M$}}}
\newcommand{\bfN}{\ensuremath{\mbox{\boldmath$N$}}}
\newcommand{\bfR}{\ensuremath{\mbox{\boldmath$R$}}}
\newcommand{\bfP}{\ensuremath{\mbox{\boldmath$P$}}}
\newcommand{\bfQ}{\ensuremath{\mbox{\boldmath$Q$}}}
\newcommand{\bfS}{\ensuremath{\mbox{\boldmath$S$}}}
\newcommand{\bfU}{\ensuremath{\mbox{\boldmath$U$}}}
\newcommand{\bfV}{\ensuremath{\mbox{\boldmath$V$}}}
\newcommand{\bfY}{\ensuremath{\mbox{\boldmath$Y$}}}
\newcommand{\bfX}{\ensuremath{\mbox{\boldmath$X$}}}
\newcommand{\bfW}{\ensuremath{\mbox{\boldmath$W$}}}
\newcommand{\bfZ}{\ensuremath{\mbox{\boldmath$Z$}}}
\newcommand{\Var}{\ensuremath{\rm Var}}
\newcommand{\E}{\ensuremath{\rm E}}
\bibliographystyle{plainnat}
\begin{document}
\title{The rmgarch models: Background and properties.\\
(Version 1.3-0)}
\author{Alexios Galanos}
\date{\today}
\maketitle
\tableofcontents
\newpage
\input{rmgarch1.tex}
\clearpage
\bibliography{rmgarchbib}
\end{document}