%\setlength\topmargin{-0.25in} \setlength\oddsidemargin{-0.25in} %\setlength\textheight{9.0in} \setlength\textwidth{7.0in} %\setlength\columnsep{0.375in} \newlength\titlebox %\setlength\titlebox{2.25in} \setlength\headheight{0pt} %\setlength\headsep{0pt} \setlength{\evensidemargin}{-0.25 in} \setlength{\oddsidemargin}{-0.25 in} \setlength{\textwidth}{6.8 in} \setlength{\topmargin}{-0.75 in} \setlength{\textheight}{9.3 in} \renewcommand{\baselinestretch}{0.9} \renewcommand{\labelenumi}{\arabic{enumi}} \renewcommand{\labelenumii}{(\alph{enumii})} \renewcommand{\labelenumiii}{(\roman{enumiii})} \makeatletter \let\orig@Itemize =\itemize \let\orig@Enumerate =\enumerate \let\orig@Description =\description % Zero the vertical spacing parameters \def\MySpacing{\itemsep=1.0ex\topsep=0.0ex\partopsep=0.0ex\parskip=0.0ex\parsep=0.0ex} \def\WideSpacing{\itemsep=2.0ex\topsep=0.5ex\partopsep=0.0ex\parskip=0.0ex\parsep=0.0ex} % Redefine the environments in terms of the original values \renewenvironment{itemize}{\orig@Itemize\MySpacing}{\endlist} \newenvironment{Myenumerate}{\orig@Enumerate\MySpacing}{\endlist} \newenvironment{enumerateWide}{\orig@Enumerate\WideSpacing}{\endlist} \renewenvironment{description}{\orig@Description\MySpacing}{\endlist} \newenvironment{qenumerate}{\parindent 0in \orig@Enumerate}{\endlist} \def\qitemize{% \ifnum \@itemdepth >\thr@@\@toodeep\else \advance\@itemdepth\@ne \edef\@itemitem{labelitem\romannumeral\the\@itemdepth}% \expandafter \list \csname\@itemitem\endcsname % {\def\makelabel##1{\hss\llap{##1}}}% {\def\makelabel##1{\llap{##1}}}% \fi} \def\hsp{\vspace{0.1 in}} \def\fsp{\vspace{0.2 in}} \makeatother \renewcommand\rmdefault{ppl} \newcommand\textsclarge[1]{\fontshape{sc}\fontsize{14}{15} \selectfont{#1}} \newcommand\textscnormal[1]{\fontshape{sc}\fontsize{12}{15} \selectfont{#1}} \newcommand{\dst}{\displaystyle} \newcommand{\bigone}{{\rm 1\hspace{-3 pt}l}} %\newcommand{\mathsfsmall}{\fontshape{sf}\fontsize{12}{15} \selectfont{#1}} %\def\transpose{{\mathsfsmall{T}}} \DeclareOldFontCommand{\sf}{\small\it\sffamily}{\mathsf} \def\transpose{{\sf{T}}} \DeclareSymbolFont{AMSb}{U}{msb}{m}{n} \DeclareMathSymbol{\N}{\mathbin}{AMSb}{"4E} \DeclareMathSymbol{\Z}{\mathbin}{AMSb}{"5A} \DeclareMathSymbol{\R}{\mathbin}{AMSb}{"52} \DeclareMathSymbol{\Q}{\mathbin}{AMSb}{"51} \DeclareMathSymbol{\I}{\mathbin}{AMSb}{"49} \DeclareMathSymbol{\C}{\mathbin}{AMSb}{"43} \def\X{\mathbb{X}} \def\CalC{\mathscr{C}} \def\P{\text{Pr}} \def\dsum#1#2{\displaystyle{\sum_{#1}^{#2}}~} \def\dint#1#2{\displaystyle{\int_{#1}^{#2}}} \def\Prob#1{\mbox{P}\left (~#1~\right )} \def\Exp#1#2{\mbox{E}_{#1} [~#2~]} \def\bigchoose#1#2{\displaystyle{#1 \choose #2}} \newcommand{\undertilde}[1]{\underset{\widetilde{}}{#1}} \newcommand\Xvec{{\skew0\utilde{X}}} \def\Xvecn{{\undertilde{X_n}}} \def\Yvec{{\utilde{Y}}} \def\Tvec{{\utilde{T}}} \def\xvec{{\utilde{x}}} \def\yvec{{\utilde{y}}} \def\zvec{{\utilde{z}}} \def\tvec{{\utilde{t}}} \def\qvec{{\utilde{q}}} \def\gvec{{\utilde{g}}} \def\hvec{{\utilde{h}}} \def\lvec{{\utilde{l}}} \def\thvec{{\skew0\utilde{\theta}}} \def\thveczero{{\skew0\utilde{\theta}_0}} \def\thvecone{{\skew0\utilde{\theta}_1}} \def\thvectwo{{\skew0\utilde{\theta}_2}} \def\phivec{{\skew0\utilde{\phi}}} \def\etavec{{\undertilde{\eta}}} \def\betavec{{\skew0\utilde{\beta}}} \def\omegavec{{\skew0\utilde{\omega}}} \def\wvec{{\undertilde{w}}} \def\Svec{{\undertilde{S}}} \def\zerovec{{\mathbf{0}}} \def\Psimat{{\bm{\Psi}}} \def\avec{{\undertilde{a}}} \def\Normal{\text{Normal}} \def\Xveca{{\skew0\utilde{X}}_1} \def\Xvecb{{\skew0\utilde{X}}_2} \def\xveca{{\skew0\utilde{x}}_1} \def\xvecb{{\skew0\utilde{x}}_2} \def\mvec{{\skew0\utilde{m}}} \def\nvec{{\skew0\utilde{n}}} \def\cvec{{\skew0\utilde{c}}} \def\fvec{{\skew0\utilde{f}}} \def\hvec{{\skew0\utilde{h}}} \def\Dvec{{\skew0\utilde{D}}} \def\xivec{{\skew0\utilde{\xi}}} \def\lvec{{\skew0\utilde{l}}} \def\lvecn{{\skew0\utilde{l}_n}} \def\dotlvec{{\skew0\utilde{\dot{l}}}} \def\dotlvecn{{\skew0\utilde{\dot{l}}_n}} \def\ddotlvecn{{\skew0\utilde{\ddot{l}}_n}} \def\dddotlvecn{{\skew0\utilde{\dddot{l}}_n}} \def\lra{\longrightarrow} \def\Lra{\Longrightarrow} \def\calA{\mathcal{A}} \def\calB{\mathcal{B}} \def\calC{\mathcal{C}} \def\calD{\mathcal{D}} \def\calE{\mathcal{E}} \def\calF{\mathcal{F}} \def\calG{\mathcal{G}} \def\calH{\mathcal{H}} \def\calS{\mathcal{S}} \def\calT{\mathcal{T}} \def\bmt{\tvec} \def\bmf{\fvec} \def\bmx{\xvec} \def\bmh{\hvec} \def\bmxzero{\xvec_0} \def\bmphi{\bm{\phi}} \def\bmphizero{\bm{\phi_0}} \def\bmth{\thvec} \def\bmphi{\bm{\phi}} \def\bmx{\bm{x}} \def\bmg{\bm{g}} \def\alphaline{\overline{\alpha}} \def\betaline{\overline{\beta}} \def\betadag{{\beta^\dag}} \def\betastar{{\beta^\star}} \def\transpose{{\textsf{T}}} \def\bmZn{\bm{Z}_n} \def\bmZ{\bm{Z}} \def\bmD{\bm{D}} %\def\dddot#1{\stackrel{\ldots}{#1}} \setcounter{section}{0} \newcounter{mytheorem} \setcounter{mytheorem}{1} \renewcommand\thesection{\arabic{section}.} \renewcommand\thesubsection{\arabic{section}.\arabic{subsection}} \def\lra{\longrightarrow} \def\Lra{\Longrightarrow} \def\Llra{\Longleftrightarrow} \def\eqdef{\stackrel{def}{=}} \def\eqdist{\stackrel{d}{=}} \def\tildethn{\skew2\tilde{\thvec}_n} \def\hatthn{\skew2\hat{\thvec}_n} \def\tildephin{\skew2\tilde{\bmphi}_n} \def\thnstar{\bm{\theta}_n^\star} \def\th{\theta} \def\Exp{\text{E}} \def\Var{\text{Var}} \newcommand{\SET}[1]{\left\{#1\right\}} \def\muX{\muvec^\text{\tiny{$X$}}} \def\muY{\muvec^\text{\tiny{$Y$}}} \def\muXgy{\muvec^\text{\tiny{$X|y$}}} \def\muXgY{\muvec^\text{\tiny{$X|Y$}}} \def\Loss{\mathcal{L}} %\newcommand\argmin[1]{\underset{#1}{\textrm{argmin}}} %\newcommand\argmax[1]{\underset{#1}{\textrm{argmax}}} \newcommand\Xbarn{{\overline{X}_n}} \newcommand\xbarn{{\overline{x}_n}} \newcommand\Xbar{{\overline{X}}} \newcommand\xbar{{\overline{x}}} \def\thetahat{\widehat{\theta}} \def\sigmahat{\widehat{\sigma}} \def\tauhat{\widehat{\tau}} \def\lambdahat{\widehat{\lambda}} \newcommand\muvec{{\skew0\undertilde{\mu}}} \newcommand\pivec{{\skew0\utilde{\pi}}} \def\lra{\longrightarrow} \def\Lra{\Longrightarrow} \def\Llra{\Longleftrightarrow} \def\iif{\Longleftrightarrow} \def\CiP{\stackrel{p}{\lra}} \def\CiR{\stackrel{r}{\lra}} \newcommand\CRM[1]{\stackrel{r = #1}{\lra}} \newcommand\Cqm{\stackrel{q.m.}{\lra}} \def\Cas{\stackrel{a.s.}{\lra}} \def\CiL{\stackrel{\mathfrak{L}}{\lra}} \def\eqdef{\stackrel{def}{=}} \def\CiD{\stackrel{d}{\lra}} \def\Cae{\stackrel{a.e.}{\lra}} \def\Cwp{\stackrel{w.p. 1}{\lra}} \def\nlra{\nrightarrow} \def\nCas{\stackrel{a.s.}{\nlra}} \def\nCiP{\stackrel{p}{\nlra}} \def\approxsim{\; \; \raisebox{-0.3ex}{.} \\ \hspace{-0.11in} \sim \\ \hspace{-0.105in} \raisebox{0.95ex}{.} \; \; } \newcommand\Xvecsub[1]{{\skew0\utilde{X}}_{\! #1}} \newcommand\Zvecsub[1]{{\skew0\utilde{Z}}_{\! #1}} \newcommand\Zvec{{\skew0\utilde{Z}}} \newcommand\Xbarvecn{{\overline{\skew0\utilde{X}}_{\!n}}} \def\Xmean{\overline{X}} \def\xmean{\overline{x}} \def\Ymean{\overline{Y}} \def\ymean{\overline{y}} \def\Xseq{X_1,\ldots,X_n} \def\xseq{x_1,\ldots,x_n} \def\Yseq{Y_1,\ldots,Y_n} \def\yseq{y_1,\ldots,y_n} \def\Zseq{Z_1,\ldots,Z_n} \def\zseq{z_1,\ldots,z_n} \def\eqindist{\stackrel{d}{=}} \def\O{\text{O}} \def\o{\text{o}} \def\E{\text{E}} \def\Var{\text{Var}} \def\Cov{\text{Cov}} \def\Cramer{Cram\'{e}r} \def\FisherI{\mathcal{I}} \def\FisherItilde{\widetilde{\mathcal{I}}} \def\MSE{\text{MSE}} \def\calR{\mathcal{R}} \def\calW{\mathcal{W}} \def\calX{\mathcal{X}} \def\calH{\mathcal{H}} \def\thetapr{\theta^\prime} \def\boldl{\lvec} \def\thnstar{\thvec_n^\star} \def\tildethn{\skew2\widetilde{\thvec}_n} \def\hatthn{\skew2\hat{\thvec}_n} \def\tildephin{\skew2\widetilde{\bmphi}_n} \def\thnstar{\bm{\theta}_n^\star} \def\thtilde{\widetilde{\thvec}_n} \def\thhat{\widehat{\thvec}_n} \def\thhatzero{\widehat{\thvec}_{n0}} \def\thhatone{\widehat{\thvec}_{n1}} %\def\thhatzeroone{\widehat{\thvec}_{n01}} \def\thhatzeroone{{\skew0\utilde{\widehat{\theta}}_{n01}}} \def\thhatonezero{{\skew0\utilde{\widehat{\theta}}_{n10}}} \def\thhatoneone{{\skew0\utilde{\widehat{\theta}}_{n11}}} \def\thtilzero{\widetilde{\thvec}_{n0}} \def\thtilone{\widetilde{\thvec}_{n1}} \def\thtilzeroone{{\skew0\utilde{\widetilde{\theta}}_{n01}}} \def\thtilonezero{{\skew0\utilde{\widetilde{\theta}}_{n10}}} \def\thtiloneone{{\skew0\utilde{\widetilde{\theta}}_{n11}}} \def\dotlike{\dot{\bm{l}}_n} \def\ddotlike{\ddot{\bm{l}}_n} \def\thhatNewt{\widehat{\thvec}^{\dagger}} \def\thhatScor{\widehat{\thvec}^{\star}} \def\thddag{{\thvec}_n^{\ddag}} \def\Ind{\mathbb{I}} \def\Fisher{\mathcal{I}} \def\FisherIhat{\widehat{I}_n} \def\FisherIhatzzo{\widehat{I}_{n00.1}} \def\FisherIhatzz{\widehat{I}_{n00}} \def\FisherIhatzo{\widehat{I}_{n01}} \def\FisherIhatoz{\widehat{I}_{n10}} \def\FisherIhatoo{\widehat{I}_{n11}} \def\xtilde{\widetilde{x}} \def\Xtilde{\widetilde{X}} \def\bth{\thvec} \def\bx{\mathbf{x}} \def\bX{\mathbf{X}} \def\xbar{\overline{x}} \def\xmean{\overline{x}} \def\Xmedian{\widetilde{X}} \def\bY{\mathbf{Y}} \def\bU{\mathbf{U}} \def\bD{\mathbf{D}} \def\Xhat{\widehat{X}} \def\Zhat{\widehat{Z}} \def\by{\mathbf{y}} \def\bY{\mathbf{Y}} \def\ybar{\overline{y}} \def\ymean{\overline{y}} \def\zmean{\overline{z}} \def\Zmean{\overline{Z}} \def\Ymean{\overline{Y}} \def\Fhat{\widehat{F}} \def\Fhatn{\widehat{F}_n} \def\shat{\widehat{s}} \def\sehat{\widehat{\text{se}}} \def\se{\text{se}} \def\O{\text{O}} \def\o{\text{o}} \renewcommand\textsclarge[1]{\fontshape{sc}\fontsize{14}{15} \selectfont{#1}} \renewcommand\textscnormal[1]{\fontshape{sc}\fontsize{12}{15} \selectfont{#1}} \newcommand\argmin[1]{\underset{#1}{\textrm{argmin}}} \newcommand\argmax[1]{\underset{#1}{\textrm{argmax}}} \def\omegavec{{\omega}} \def\lra{\longrightarrow} \def\Lra{\Longrightarrow} \def\Xseq{X_1,\ldots,X_m} \def\Yseq{Y_1,\ldots,Y_n} \def\Zerovec{\bm{0}} \def\thetavec{{\theta}} \def\leqM{\stackrel{p}{<=}} \def\Rpackold{\texttt{R}} \def\Rpacknew{{\rotatebox{-0}{\vspace{0.5 in}\begin{figure}\includegraphics[scale=0.6]{Rlogo.ps}\end{figure}}}} \def\Rpack{\textcolor[rgb]{0.23,0.49,0.77}{{\Large \textsf{R}}}} \def\Ident{\mathbf{I}} \def\thetahat{\widehat{\theta}} \def\varthetahat{\widehat{\vartheta}} \def\betahat{\widehat{\beta}} \def\phihat{\widehat{\phi}} \def\betatilde{\widetilde{\beta}} \def\mutilde{\widetilde{\mu}} \def\E{\mathbb{E}} \def\Var{\mathbb{V}ar} \def\Cov{\mathbb{C}ov} \def\C{\mathbb{C}} \def\Corr{\mathbb{C}orr} \def\P{\mathbb{P}} \def\R{\mathbb{R}} \def\IID{\text{IID}} \def\WN{\text{WN}} \def\MA{\text{MA}} \def\AR{\text{AR}} \def\SMA{\text{SMA}} \def\SAR{\text{SAR}} \def\calJ{\mathcal{J}} \def\calN{\mathcal{N}} \def\calL{\mathcal{L}} \def\calH{\mathcal{H}} \def\calS{\mathcal{S}} \def\calh{\mathpzc{h}} \def\Fisher{\mathcal{I}} \def\Ind{\mathds{1}} \def\Fhatn{\widehat{F}_n} \def\lra{\longrightarrow} \def\CiD{\stackrel{d}{\longrightarrow}} \def\CiP{\stackrel{p}{\longrightarrow}} \def\Cas{\stackrel{a.s.}{\longrightarrow}} \def\transposeold{{\sf{T}}} \def\transposex{\intercal} \def\transpose{\top} \def\Xvec{{\skew0\bm{X}}} \def\Xveca{{\skew0\mathbf{X}}_1} \def\Xvecb{{\skew0\mathbf{X}}_2} \def\bXa{{\skew0\mathbf{X}}_1} \def\bXb{{\skew0\mathbf{X}}_2} \def\Yvec{{\skew0\bm{Y}}} \def\xvec{{\skew0\bm{x}}} \def\xveca{{\skew0\mathbf{x}}_1} \def\xvecb{{\skew0\mathbf{x}}_2} \def\bxa{{\skew0\mathbf{x}}_1} \def\bxb{{\skew0\mathbf{x}}_2} \def\mvec{{\skew0\mathbf{m}}} \def\muvec{{\skew0\bm{\mu}}} \def\bmu{{\bm{\mu}}} \def\pitilde{\widetilde{\pi}} \def\ptilde{\widetilde{p}} \def\phat{\widehat{p}} \def\Lhat{\widehat{L}} \def\What{\widehat{W}} \def\cvec{{\skew0\mathbf{c}}} \def\Xbar{\overline{X}} \def\xbar{\overline{x}} \def\ybar{\overline{y}} \def\yhat{\hat{y}} \def\betahat{\widehat{\beta}} \def\betavec{\utilde{\beta}} \def\betahatvec{\skew3\widehat{\utilde{\beta}}} \def\sigmahat{\widehat{\sigma}} \def\ehat{\widehat{e}} \def\zhat{\widehat{z}} \def\nhat{\widehat{n}} \def\xbarA{\overline{x}_A} \def\xbarB{\overline{x}_B} \def\calR{\mathcal{R}} \def\calX{\mathcal{X}} \def\calS{\mathcal{S}} \def\bhatint{\widehat{\beta}_0} \def\bhatsl{\widehat{\beta}_1} \def\ahat{\widehat{a}} \def\bhat{\widehat{b}} \def\chat{\widehat{c}} \def\ghat{\widehat{g}} \def\lhat{\widehat{l}} \def\uhat{\widehat{u}} \def\Ihat{\widehat{I}} \def\Itilde{\widetilde{I}} \def\Icheck{\widecheck{I}} \def\rhohat{\widehat{\rho}} \def\pihat{\widehat{\pi}} \def\btilde{\widetilde{b}} \def\bjack{\widehat{b}_{\text{JACK}}} \def\One{\mathbf{1}} \def\Zero{\mathbf{0}} \newcommand\xbarBi[1]{\overline{x^{\text{\tiny{(B)}}}_{#1}}} \newcommand\xbarib[1]{\overline{x^{\text{\tiny{(B)}}}_{#1}}} \def\Fstat{\frac{(SSE_R - SSE_C)/(k-g)}{SSE_C/(n-k-1)}} \def\approxsim{\sim \! \! \! : \;} \def\hsp{\vspace{0.1 in}} \def\fsp{\vspace{0.2 in}} %\def\dfrac#1#2{{\displaystyle {#1 \over #2}}}% \def\dint{\mathop{\displaystyle \int}}% \def\dsum{\mathop{\displaystyle \sum}}% %\renewenvironment{proof}[1][\proofname]{\par % \pushQED{\qed}% % \normalfont \topsep6\p@\@plus6\p@\relax % \trivlist % \item[\hskip\labelsep % \itshape % #1\@addpunct{.}]\ignorespaces %}{% % \popQED\endtrivlist\@endpefalse %} %\providecommand{\proofname}{Proof} \def\sectitle{\thesection.~\insertsectionhead} \def\subsectitle{\thesection.\thesubsection~\insertsubsectionhead} \def\xhat{\widehat x} \def\Xhat{\widehat X} \def\Rhat{\widehat R} \def\what{\widehat w} \def\muhat{\widehat \mu} \def\gammahat{\widehat \gamma} \def\Gammahat{\widehat \Gamma} \def\phihat{\widehat \phi} \def\Pred{\widehat P} \def\Ptil{\widetilde P} \def\Z{\mathbb{Z}} \def\ARMA{\text{ARMA}} \def\SARMA{\text{SARMA}} \def\ARIMA{\text{ARIMA}} \def\SARIMA{\text{SARIMA}} \def\phivec{\utilde\phi} \def\rhovec{\rho} \def\tR{{\scriptscriptstyle \text{R}}} \def\tF{{\scriptscriptstyle \text{F}}} \def\tB{{\scriptscriptstyle \text{B}}} \def\B{\text{B}} \def\bA{\mathbf{A}} \def\bV{\mathbf{V}} \def\bD{\mathbf{D}} \def\bz{\mathbf{z}} \def\bZ{\mathbf{Z}} \def\bv{\mathbf{v}} \def\br{\mathbf{r}} \def\be{\mathbf{e}} \def\bb{\mathbf{b}} \def\bc{\mathbf{c}} \def\bd{\mathbf{d}} \def\bu{\mathbf{u}} \def\bw{\mathbf{w}} \def\bF{\mathbf{F}} \def\bG{\mathbf{G}} \def\bW{\mathbf{W}} \def\E{\mathbb{E}} \def\Var{\text{Var}} \def\Cov{\text{Cov}} \def\Corr{\text{Corr}} \def\Obs{\mathcal{O}} \def\Exp{\mathcal{E}}