{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courie r" 1 10 255 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 } {PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Outpu t" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 } 1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "# Must include funct ion library: open and compile library.mws first." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "# Zero mean ARCH(p) \n# Generate observed dat a y" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "t := 't':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "T := 40:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 12 "BurnIn := T:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "a := [0.1,0.6]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 " p := nops(a):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "errors := \+ stats[random, normald[0,1]](T):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "alpha := 'alpha':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "y := ARCH(T+BurnIn,p,a):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "plot_series(BurnIn,T+BurnIn,y);" }}{PARA 13 "" 1 "" {GLPLOT2D 516 312 312 {PLOTDATA 2 "6%-%'CURVESG6#7J7$$\"\"\"\"\"!$!+:LmJX!#57$$ \"\"#F*$\"+>W\"Ho\"F-7$$\"\"$F*$\"+S&f56#F-7$$\"\"%F*$!+M2A?5F-7$$\"\" &F*$!+Z8%**\\\"F-7$$\"\"'F*$!+Mas!4)!#67$$\"\"(F*$\"+C`0\\KF-7$$\"\")F *$\"+o/>(G*FG7$$\"\"*F*$\"+R7\"[[&FG7$$\"#5F*$\"+k'=Wb$F-7$$\"#6F*$!+L \\[8@F-7$$\"#7F*$!+g:T[UFG7$$\"#8F*$\"+C'f'=?F-7$$\"#9F*$\"+h#G$RCF-7$ $\"#:F*$\"+&>\"*e$HF-7$$\"#;F*$\"+!*Q1jTF-7$$\"#F*$\"+-lfoJF-7$$\"#?F*$!+V,YF-7$$\"#LF*$!+U@\"G(>F-7$$\"#MF*$\"+HgZTH?F--%&STYLEG6#%%LINEG-%'COLOURG6 &%$RGBGF*F*F*" 1 6 0 1 10 0 2 6 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "currentdir( \"C:\\\\ARCH\\\\test\\\\\"):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "#ExportARCH(\"test.dat\", y):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "#currentdir();" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "#y := ImportARCH(\"joe.dat\"):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "#T := nops(y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "#generateData(5,40,2,[0.5,0.5]): #N,T,p,alpha" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "#plot_series(T,ARCH(T,nops(op(2,arc h4)),arch4));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "#MSPE(T,y, 2,[0.1,0.95]);\n#VarCov(T,y,arch2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "T0 := BurnIn:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 286 "#arch1 := ARCH_score(T0,T,y,[0.5],5);\narch2 := ARCH_score(T0 ,T,y,[0.5,0.5],5);\n#arch3 := ARCH_score(T0,T,y,[0.5,0.5,0.5],5);\n#ar ch4 := ARCH_score(T0,T,y,[0.5,0.5,0.5,0.5],5);\n#arch5 := ARCH_score(T 0,T,y,[0.5,0.5,0.5,0.5,0.5],5);\n#arch6 := ARCH_score(T0,T,y,[0.5,0.5, 0.5,0.5,0.5,0.5],3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&arch2G-%'RT ABLEG6%\"*#4Lo<-%'MATRIXG6#7$7#$\"3+-')GI.4Jf!#>7#$\"3yx!4E`-\"HE!#=&% 'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 434 "#ar ch7 := ARCH_score(T0,T,y,[0.5,0.5,0.5,0.5,0.5,0.5,0.5],5):\n#arch8 := \+ ARCH_score(T0,T,y,[0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5],5):\n#arch9 := ARC H_score(T0,T,y,[0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5],5):\n#arch10 := A RCH_score(T0,T,y,[0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5],5):\n#arch1 1 := ARCH_score(T0,T,y,[0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5],5 ):\n#arch12 := ARCH_score(T0,T,y,[0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5, 0.5,0.5,0.5],5):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "#plot_s eries2(T,y,ARCH(T0,T,nops(op(1,arch2)),arch2)):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 101 "#alpha_estimates := [a rch1,arch2,arch3,arch4,arch5,arch6,arch7,arch8,arch9,arch10]: #,arch11 ,arch12]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "#alpha_estimat es := [arch1,arch2,arch3,arch4,arch5,arch6,arch7,arch8]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "alpha_estimates := array(1..8);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%0alpha_estimatesG-%&arrayG6$;\"\"\" \"\")7\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "alpha_estimates [2] := arch2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%0alpha_estimatesG6 #\"\"#-%'RTABLEG6%\"*#4Lo<-%'MATRIXG6#7$7#$\"3+-')GI.4Jf!#>7#$\"3yx!4E `-\"HE!#=&%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 325 "#currentdir(\"C :\\\\ARCH\\\\arch2-200-200\\\\\"):\n#p := 2: T := 200: T0 := T: n := 1 2: pmax := 8:\n#y := 'y': errors := 'errors':\n#y := ImportArray(cat( \"arch\",p,\"-\",T,\"-\",n,\".dat\")):\n#errors := ImportArray(cat(\"a rch\",p,\"-\",T,\"-\",n,\"-errors.dat\")):\n#alpha_estimates := Import AlphaEstimates(cat(\"arch\",p,\"-\",T,\"-\",n,\"-estimates.dat\")):\n " }}}{EXCHG {PARA 12 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 67 "#L(T0,T,y,arch2); L(T0,T,y,convert([.1,.9], Vector) ); f(y,[.1,.9]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "#Envelop e" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "#prior*likelihood" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "lamda := 1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "e := (x,B,lamda) -> evalf(lamda * e xp(lamda*(B-x)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"eGf*6%%\"xG% \"BG%&lamdaG6\"6$%)operatorG%&arrowGF*-%&evalfG6#*&9&\"\"\"-%$expG6#*& F2F3,&9%F39$!\"\"F3F3F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plot(e(x,0,1),x=0..1);" }}{PARA 13 "" 1 "" {GLPLOT2D 472 292 292 {PLOTDATA 2 "6%-%'CURVESG6$7S7$$\"\"!F)$\"\"\"F)7$$\"3emmm;arz@!#>$\"3 qwzLroQ%y*!#=7$$\"3[LL$e9ui2%F/$\"3&\\AZi%)o0g*F27$$\"3nmmm\"z_\"4iF/$ \"3-()H0_'ozR*F27$$\"3[mmmT&phN)F/$\"3q@-e`LM)>*F27$$\"3CLLe*=)H\\5F2$ \"3K-P;0r(Q+*F27$$\"3gmm\"z/3uC\"F2$\"3D!)p*>rcs#))F27$$\"3%)***\\7LRD X\"F2$\"3qR\\$=jE![')F27$$\"3]mm\"zR'ok;F2$\"3)ot'>wO\\m%)F27$$\"3w*** \\i5`h(=F2$\"3ku.Ey_L*G)F27$$\"3WLLL3En$4#F2$\"3zN,nmH(46)F27$$\"3qmm; /RE&G#F2$\"3!oRI$zH0dzF27$$\"3\")*****\\K]4]#F2$\"3#z>E?vnsy(F27$$\"3$ ******\\PAvr#F2$\"3;F#=RVI/i(F27$$\"3)******\\nHi#HF2$\"3!4![@$oMIY(F2 7$$\"3jmm\"z*ev:JF2$\"3]4E%faAHK(F27$$\"3?LLL347TLF2$\"3=gDgO_tfrF27$$ \"3,LLLLY.KNF2$\"3Kh(4AfUV-(F27$$\"3w***\\7o7Tv$F2$\"3IOaMnn1qoF27$$\" 3'GLLLQ*o]RF2$\"3]^bq%)fLOnF27$$\"3A++D\"=lj;%F2$\"37!eOk00Ef'F27$$\"3 1++vV&R'F27$$\"3cmm;/T1&*\\F2$\"3s_8D36IogF27$$\"3& em;zRQb@&F2$\"3<))yCcZ(f$fF27$$\"3\\***\\(=>Y2aF2$\"3l'R.csNJ#eF27$$\" 39mm;zXu9cF2$\"3EY@H2Yn.dF27$$\"3l******\\y))GeF2$\"3aOc7XF$Ge&F27$$\" 3'*)***\\i_QQgF2$\"3y4XFi/4naF27$$\"3@***\\7y%3TiF2$\"3s)*[q&Q)Qd`F27$ $\"35****\\P![hY'F2$\"3\"og2v)*f\"Q_F27$$\"3kKLL$Qx$omF2$\"3KPiAaHHL^F 27$$\"3!)*****\\P+V)oF2$\"3#[%*o9VTO-&F27$$\"3?mm\"zpe*zqF2$\"3p%[DY/0 j#\\F27$$\"3%)*****\\#\\'QH(F2$\"3:Dq\"eNZ?#[F27$$\"3GKLe9S8&\\(F2$\"3 e%>)[:Y'fs%F27$$\"3R***\\i?=bq(F2$\"3cMlK'Qwvi%F27$$\"3\"HLL$3s?6zF2$ \"3%4:n(oWOLXF27$$\"3a***\\7`Wl7)F2$\"3e8-:sxyOWF27$$\"3#pmmm'*RRL)F2$ \"31FuI^%=dM%F27$$\"3Qmm;a<.Y&)F2$\"3QDU'R()>XD%F27$$\"3=LLe9tOc()F2$ \"3A3T-]n'f;%F27$$\"3u******\\Qk\\*)F2$\"3u6h+q'*RF27$$\"3ImmmmxGp$*F2$\"3'*=3][QH=RF27$$\"3A++D\"oK0e*F 2$\"3_g,p<+ROQF27$$\"3A++v=5s#y*F2$\"3OIj)ye,'fPF27$F*$\"3MBWr6WzyOF2- %'COLOURG6&%$RGBG$\"#5!\"\"F(F(-%+AXESLABELSG6$Q\"x6\"Q!Fa[l-%%VIEWG6$ ;F(F*%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 464 " h3 := (p ,alpha) -> ((1-add(alpha[i], i=2..p))/max(0.0000000001,alpha[1]) )^(1/ 2);\n h2 := (p,alpha) -> `if`(p>1,(p-1)!,1):\n h := (p,alpha) -> 1/((. 99/p)^p);\nlogf := (y,alpha) -> evalf(-(T/2)*log(2*Pi)-1/2*Sum(log(u(t ,alpha)),t=BurnIn+1..T+BurnIn)-(1/2)*Sum(y[t]^2/u(t,alpha),t=BurnIn+1. .T+BurnIn)):\nf := (y,alpha) -> evalf(Product((1/(sqrt(2*Pi*u(t,alpha) )))*(exp((-y[t]^2)/(2*u(t,alpha)))) , t=BurnIn+1..T+BurnIn));\nu := (t ,alpha) -> alpha[1] + alpha[2]*y[t-1]^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#h3Gf*6$%\"pG%&alphaG6\"6$%)operatorG%&arrowGF)*$*&,&\"\"\"F0- %$addG6$&9%6#%\"iG/F7;\"\"#9$!\"\"F0-%$maxG6$$F0!#5&F56#F0F<#F0F:F)F)F )" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hGf*6$%\"pG%&alphaG6\"6$%)ope ratorG%&arrowGF)*&\"\"\"F.)*&$\"#**!\"#F.9$!\"\"F4F5F)F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"yG%&alphaG6\"6$%)operatorG%&arr owGF)-%&evalfG6#-%(ProductG6$*&-%%sqrtG6#,$*(\"\"#\"\"\"%#PiGF:-%\"uG6 $%\"tG9%F:F:!\"\"-%$expG6#,$*&#F:F9F:*&&9$6#F?F9F%\"uG f*6$%\"tG%&alphaG6\"6$%)operatorG%&arrowGF),&&9%6#\"\"\"F1*&&F/6#\"\"# F1)&%\"yG6#,&9$F1F1!\"\"F5F1F1F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 " h(2,alpha_estimates[2])*logf(y,alpha_estimates[2]); " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "l_ml := h(2,alpha_estimates[2]) *log(f(y,alpha_estimates[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+U !o/G#!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%l_mlG$!+G!o/G#!\")" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "convert(alpha_estimates[2], list);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"3+-')GI.4Jf!#>$\"3yx!4E `-\"HE!#=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "log(likelihood (BurnIn,T,y,convert([.911655924787905109e-1,.365230713975917166],Vecto r)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+)*f#y(p!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "log(f(y,alpha_estimates[2]));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$!+'y;xe&!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "log(likelihood(BurnIn,T,y,alpha_estimates[2])); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+'y;xe&!\"*" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 33 "L(BurnIn,T,y,alpha_estimates[2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!*#or(e&!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "with(St atistics): with(stats); with(stats[statplots]);" }}{PARA 7 "" 1 "" {TEXT -1 116 "Warning, these names have been redefined: anova, describ e, fit, importdata, random, statevalf, statplots, transform\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7*%&anovaG%)describeG%$fitG%+importdat aG%'randomG%*statevalfG%*statplotsG%*transformG" }}{PARA 7 "" 1 "" {TEXT -1 158 "Warning, these names have been redefined: boxplot, histo gram, scatterplot, xscale, xshift, xyexchange, xzexchange, yscale, ysh ift, yzexchange, zscale, zshift\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7 .%(boxplotG%*histogramG%,scatterplotG%'xscaleG%'xshiftG%+xyexchangeG%+ xzexchangeG%'yscaleG%'yshiftG%+yzexchangeG%'zscaleG%'zshiftG" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "EXP := Distribution(PDF = (x -> piecewise(x<0,0,lamda*exp((B-x)*lamda)))):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 25 "E := RandomVariable(EXP):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 85 "#plot3d(E(a0,-2)*E(a1,1)+f(y,alpha_estimates [2]),a0=0..2,a1=0..2,color=red,axes=boxed" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 129 "display(\{\nplot3d(e(a0,1,1/10)*e(a1,1,1/10)+h(2,a lpha_estimates[2])*f(y,alpha_estimates[2])/2, a0=0.1..5,a1=0.1..5,axes =boxed)\n\});" }}{PARA 13 "" 1 "" {GLPLOT3D 488 416 416 {PLOTDATA 3 "6 %-%%GRIDG6%;$\"\"\"!\"\"$\"\"&\"\"!F&X,%)anythingG6\"6\"[gl'!%\"!!#\\b m\":\":3F9414FDA73255033F93D5906D2DB7CB3F93976B5940630D3F935A87C9AE58B 73F931EDF3F0B202B3F92E46B5B88432F3F92AB25E24761413F927308B6AFC6BB3F923 C0DDBC775A53F92062F738F8E533F91D167BE6406623F919DB11A5E9CFA3F916B0602B CFB8D3F9139610F49F2B93F9108BCF3C9C30E3F90D9147F6962313F90AA629C30ACAA3 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1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 119 "#plot(h(2,[a0,0.5])*f(y,[a0,0.5]),a0=0.1..50, color=brown),\n#plot(h(2,[0.5,a0])*f(y,[0.5,a0]),a0=0.1..50, color=bl ack)\n" }}}{EXCHG {PARA 12 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 27 "B := alpha_estimates[2][1];" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"BG$\"3+-')GI.4Jf!#>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "alpha_estimates[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#-%'RTABLEG6%\"*#4Lo<-%'MATRIXG6#7$7#$\"3+-')GI.4Jf!#>7#$\"3yx!4E`-\" HE!#=&%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "h(2,alpha_estimates[2])*logf(y,alpha_estimates[2]);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$!+U!o/G#!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "l_ml := h(2,alpha_estimates[2])*log(f(y,alpha_estimat es[2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%l_mlG$!+G!o/G#!\")" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 51 "posterior := (alpha) -> h(2,alpha)*log(f(y,alpha)): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "g := (alpha) -> envelop e(alpha,B,lamda,l_ml):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "g ([0.5,0.5]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "envelope := (alpha,B,lamda,post_ml) -> e(alpha[1],B,lamda)*e(alpha[2],B,lamda)+3/ 4*post_ml:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "checkEnvelope (posterior,g,0.1,1,.05);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7\"" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "alpha_estimates[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#-%'RTABLEG6%\"*#4Lo<-%'MATRIXG6#7$7#$\"3+-')GI.4Jf!#>7#$\"3yx!4E`-\" HE!#=&%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "L(BurnIn,T,y,convert([0.5,0.5],Vector));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+)R%HBF!\")" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "lamda := 1: vB := alpha_esti mates[2]: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "#posterior := (alpha,y) -> h(2,alpha)*log(f(y,alpha)):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 73 "posterior := (alpha,y) -> h(2,alpha)*L(BurnIn,T,y,c onvert(alpha,Vector)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "e nvelope_ml := posterior(alpha_estimates[2],y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,envelope_mlG$!+U!o/G#!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "a0lb := 0.05: a0ub := 1: a1lb := 0.05: a1ub := 5: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 318 "a0 := 'a0': a1 := 'a1' : \ndisplay(\{\nplot3d(e(a0,vB[1],lamda)*e(a1,vB[2],lamda)+3/4*posteri or(alpha_estimates[2],y), a0=a0lb..a0ub,a1=a1lb..a1ub,axes=boxed, colo r=red),\nplot3d(posterior([a0,a1],y),a0=a0lb..a0ub,a1=a1lb..a1ub,axes= boxed)\n#plot3d(h3(2,[a0,a1])*log(f(y,[a0,a1])),a0=a0lb..a0ub,a1=a1lb. .a1ub,axes=boxed)\n\});" }}{PARA 13 "" 1 "" {GLPLOT3D 624 624 624 {PLOTDATA 3 "6&-%%GRIDG6%;$\"\"&!\"#$\"\"\"\"\"!;F'$F(F,X,%)anythingG6 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A71E3FBD0CFCC063AE443721E3A3C063B55AEA2ED719C063BC62CB911B4CC063C35C47 C3BB42C063CA47C5887B02C063D125A6552B8DC063D7F646B6BEB2C063DEB9FEAB3D4A C063E57121F39DDCC063EC1C005E5A90C063F2BAE60B897EC063F94E1BAB2355C063FF D5E6B60FF5C064065289A27EA5C0640CC4441400A4C064132B5307CF01C0641987F0FD 993CC0641FDA561D2FD3C0642622B85954E5C0642C614B8FF574C064329641A8061CC0 6438C1CAAD3920-%+AXESLABELSG6%%#a0G%#a1GQ!F0-%*AXESSTYLEG6#%$BOXG" 1 2 0 1 10 0 2 1 1 2 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 14 "# MMLD Msg Len" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "# parameters\nh := (p,alpha) -> 1/((.99/p)^p): #prio r\np := 2: #model order \nT := T:\nT0 := T:\nalpha_ml := alpha_estimat es[2]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 779 "\n# reduce N to \+ use only a subset of samples from envelope (keep others for later use) \nN := 1/envelopeSampleSize: \ni := 'i':\n \nposterior := (alpha) -> h (p,alpha)*L(T0,T,y,convert(alpha,Vector)):\n\n# ensure distribution is offset to cover posterior appropriately\nenvelope_ml := h(2,alpha_est imates[2])*3/4*log(f(y,alpha_estimates[2]));\n\n# check envelope for a ny collisions (slow, just assume it does?)\n#envelope := (alpha,p,B,la mda,post_ml) -> Product(e(alpha[i],B,lamda), i=1..p)+envelope_ml:\n#e \+ := (x,B,lamda) -> evalf(lamda * exp(lamda*(B-x)));\n#g := (alpha) -> e nvelope(alpha,B,lamda,envelope_ml):\n#checkEnvelope(posterior,g,0.1,1, .05):\n\n\n# generate points from envelope dist\n\n# vB := alpha_ml: v Lamda := []:\nenvelopeSampleSize := 100:\nSampleExp(envelopeSampleSize ,p,vB,vLamda);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%,envelope_mlG$!+@5 N5 " 0 "" {MPLTEXT 1 0 5 "?fill" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 560 "# F IND c\nratio := []: # keep ratios for later use\nmaxS := posterior(pts [1],y)/(PDF(E,pts[1][1],numeric)*PDF(E,pts[1][2],numeric)+envelope_ml) :\nfor i from 1 to N do\n ratio := [op(ratio),posterior(pts[i],y)/ (PDF(E,pts[i][1],numeric)*PDF(E,pts[i][2],numeric)+envelope_ml)]:\n \+ if(evalb(ratio[i]>maxS)) then \n maxS := ratio[i]:\n end \+ if:\nend do:\nmaxS;\n# Generate Sample S from posterior\nS := []:\nfor i from 1 to N do\n U := stats[random, uniform[0,1]]():\n if(eva lb(U <= ratio[i]*(1/maxS))) then \n S := [op(S),pts[i]]:\n end if: \nend do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+g)ydg%!\")" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "nops(S);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$U\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "S0 \+ := S:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "# Sort S in terms \+ of likelihood" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "#Sf := map 2(f,y,S):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 181 "# map likelih oods of S to Sf for sorting\nSf := []:\nfor i from 1 to nops(S) do\n \+ #Sf := [op(Sf), log(f(y,S[i]))]: \n Sf := [op(Sf), L(BurnIn,T,y, convert(S[i],Vector))]: \nend do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "Sf:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "\n# \+ sort S according to their likelihoods\nSsorted := SortSample(S,Sf,nops (Sf)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "nops(Ssorted);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$U\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 727 " # TODO fix to use library likeklihood functions\n# \+ Fitzgibbon (2004) Algorithm 6.1\n# find subset Q of S S := Ssorted:\ni := 'i':\nS := Ssorted:\nnit := evalf(log[2](exp(1))):\nfirstNumer := \+ 1/f(y,S[1]):\nfirstDenom := add(1/f(y,S[i]),i=1..nops(S)):\nsecondNume r := -firstNumer * logf(y,S[1]):\nsecondDenom := firstNumer:\nsecondLe ngth := secondNumer / secondDenom:\nQ := []:\nQ := [op(Q),S[1]]:\ni := 2:\nwhile ( i < nops(S) and -logf(y,S[i]) <= secondLength + 1 ) do\n oneOnF := 1/f(y,S[1]):\n firstNumer := firstNumer + oneOnF: \n secondNumer := secondNumer - oneOnF * logf(y,S[i]):\n sec ondDenom := secondDenom + oneOnF:\n secondLength := secondNumer / secondDenom:\n Q := [op(Q),S[i]]:\n i := i + 1:\nend do:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "Q;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&7$$\"3+2_iW\">=g%!#>$\"3!4hW\\7vl_)!#=7$$\"3))HO\"QX@ 7q*F'$\"3e\")=#[s%f$e#F*7$$\"3\"z2*>V5wG5F*$\"3A@&oHPjwx\"F*7$$\"3Acpb .F)o;\"F*$\"3gL^S'H$ff)*F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "nops(Q);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "add(-logf(y,Q[i]),i=1..nops(Q))/nops(Q); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+!eq6(p!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "-logf(y,alpha_estimates[2]);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"*#or(e&!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 439 "# MMLD Message Length\n# Fitzgibbon (2004) Equation \+ 6.9\nfirstNumer := add(1/f(y,Q[i]), i=1..nops(Q)):\nfirstDenom := add( 1/f(y,S[i]), i=1..nops(S)): # USE firstDenom from when finding Q?\nsec ondNumer := add(-logf(y,Q[i])/f(y,Q[i]), i=1..nops(Q)): # could use \+ f(y,Q[i]) then log(f(.)) instead of calculating f(.) twice\nsecondDeno m := firstNumer:\nmsglen := -log(firstNumer/firstDenom) + secondNumer/ secondDenom; # plus log(p) - number of lags" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'msglenG$\"+XH;#Q#!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 696 "# Rand om Coding of Estimates \n# Wallace (2005) Section 4.10.1\n\n# generate sample from prior (use S from before, weighting by 1/likelihood )\nSp rime := []:\nfor i from 1 to nops(S) do\n Sprime := [op(Sprime),-S[ i]*L(BurnIn, T,y,convert(S[i],Vector))]:\nend do:\n\n# get first rando m element in Sprime that is in the region R \n# last element in q is f inal contour\n# therefore, grab first random sample s from S that -log (f(y,s)) < - avg log f(y,Q) + 1\nboundary := add(-L(BurnIn,T,y,convert (Q[i],Vector)), i=1..nops(Q))/nops(Q) + 1;\n\ni := Generate(integer(ra nge=1..nops(S))):\nwhile ( -L(BurnIn,T,y,convert(Sprime[i],Vector)) > \+ boundary) do\n i := Generate(integer(range=1..nops(S))):\nend do: \n" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%)boundary G$\"+#eq6(z!\"*" }}{PARA 8 "" 1 "" {TEXT -1 34 "Error, invalid subscri pt selector\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 671 "\n# gener ate new samples from prior then weight by prior\nn0 := 1000: N := 2000 :\n\ni := 'i':\nratio := []: # keep ratios for later use\nmaxS := post erior(pts[1],y)/(PDF(E,pts[1][1],numeric)*PDF(E,pts[1][2],numeric)+env elope_ml):\nfor i from n0+1 to N do\n ratio := [op(ratio),posterio r(pts[i],y)/(PDF(E,pts[i][1],numeric)*PDF(E,pts[i][2],numeric)+envelop e_ml)]:\n if(evalb(ratio[i-n0]>maxS)) then \n maxS := ratio [i-n0]:\n end if:\nend do:\nmaxS;\n# Generate Sample S from poster ior\nSprime := []:\nfor i from n0+1 to N do\n U := stats[random, un iform[0,1]]():\n if(evalb(U <= ratio[i-n0]*(1/maxS))) then \n \+ Sprime := [op(Sprime),pts[i]]:\n end if: \nend do:" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+RR6o@!\")" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 13 "nops(Sprime);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$p#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 147 "\n# weight by 1/likelihood\nfor i from 1 to nops(Sprime) do\n Sprime := [op(Spri me),-Sprime[i]*L(BurnIn, T,y,convert(Sprime[i],Vector))]:\nend do:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "-log(f(y,Sprime[236]));Sp rime[236];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+&R7=t\"!\")" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"3)4\")Qt,;CX#!#=$\"3qU*=Ciz+U'F& " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "boundary;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"+#eq6(z!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 226 "\ni := Generate(integer(range=1..nops(Sprime))):\nco unt := 0:\nwhile ( -L(BurnIn,T,y,convert(Sprime[i],Vector)) > boundary ) do\n i := Generate(integer(range=1..nops(Sprime))):\nend do: \+ \ni;\nSprime[i];\n-log(f(y,Sprime[i]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"$K\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"3xb@v!)o 93R!#>$\"3O5(yPEDla)!#=" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+9yqOh! \"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "Sprime[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$$\"+r/JlP!#5$\"+_!oEU)F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "-L(BurnIn,T,y,convert(Sprime[10],Vector)) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+\"*)fbk%!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "Sprime:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 12 "" 1 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "?randi" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 " with(RandomTools):\nGenerate(integer);" }{TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"-$H=GOg&" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Generate(integer(range=2.. 7));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 10 "pmax := 8:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "order_choice(\"BIC\",T0,T,y,alpha_estimates,pmax);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#7%Q$BIC6\"\"\"$$\"+S0IV]!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "order_choice(\"AIC\",T0,T,y,alpha_estimates ,pmax);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%Q$AIC6\"\"\"$$\"+S0IV]!\" *" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "order_choice(\"AICc\", T0,T,y,alpha_estimates,pmax);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%Q%A ICc6\"\"\"$$\"+S0IV]!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "order_choice(\"HQ\",T0,T,y,alpha_estimates,pmax);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#7%Q#HQ6\"\"\"$$\"+S0IV]!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "order_choice(\"MML\",T0,T,y,alpha_estimates,pmax );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%Q$MML6\"\"\"#$\"+X#R%\\a!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "p; alpha_hat;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%' RTABLEG6%\"*;bdv\"-%'MATRIXG6#7$7#$\"3zdNO46#=^\"!#=7#$\"3iR[#)GdS(o$F .&%'VectorG6#%'columnG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "a dd(alpha_hat[i], i=2..p);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+HdS(o $!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "alpha_hat := alpha_ estimates[2]: p := op(1,alpha_hat):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "((1-add(alpha_hat[i], i=2..p))/alpha_hat[1])^(1/2);\n " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+K;SV?!\"*" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 256 "MML(T0,T,y,alpha_estimates[1]); MML(T0,T,y, alpha_estimates[2]); MML(T0,T,y,alpha_estimates[3]); MML(T0,T,y,alpha_ estimates[4]); MML(T0,T,y,alpha_estimates[5]); MML(T0,T,y,alpha_estima tes[6]);\nMML(T0,T,y,alpha_estimates[7]); MML(T0,T,y,alpha_estimates[8 ]); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Y;5CZ!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+1f]XY!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$ \"+?,-a^!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+v:\"\\'e!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+jc@Qt!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+*H1`$y!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+O !)Q'H*!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+f&39X*!\"*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 247 "-L(T0,T,y,alpha_estimates[1 ]); -L(T0,T,y,alpha_estimates[2]); -L(T0,T,y,alpha_estimates[3]); -L(T 0,T,y,alpha_estimates[4]); -L(T0,T,y,alpha_estimates[5]); -L(T0,T,y,al pha_estimates[6]);\n-L(T0,T,y,alpha_estimates[7]); -L(T0,T,y,alpha_est imates[8]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+M`;,q!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+X#R%\\a!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+S0IV]!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+&[ ?***\\!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+l5;:d!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+I&e\"Hb!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+(33aL'!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+] ^*o&e!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 131 "Fisher(T0,T,y ,arch1); Fisher(T0,T,y,arch2); Fisher(T0,T,y,arch3); Fisher(T0,T,y,arc h4); Fisher(T0,T,y,arch5); Fisher(T0,T,y,arch6);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "Fisher(T0,T,y,arch7); Fisher(T0,T,y,arch8); Fisher(T 0,T,y,arch9); Fisher(T0,T,y,arch10); Fisher(T0,T,y,arch11); Fisher(T0, T,y,arch12);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+\"zbZZ)!#6" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+D)=Iv%!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+vJG.I!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+O( oh(H!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+(fr)>?!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+TVSN@!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+QMW16!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+&H#eDy!\") " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+%4m4\"=!\"*" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$\"+kSjOF!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+* 3d/B\"!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+u%*)3-\"!\"*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "-log(1/sqrt(Fisher(T0,T,y,ar ch10)/12));" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "-log(1/sqrt(Fisher(T 0,T,y,arch3)/12));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+dSnTI!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$!+SG+Ep!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "77 0 0" 599 }{VIEWOPTS 1 1 0 3 4 1802 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 176833092 } {RTABLE M7R0 I6RTABLE_SAVE/176833092X*%)anythingG6"6"[gl!#%!!!"#"#$"3+-')GI.4Jf!#>$"3yx!4E`- "HE!#=F& }