Paper DMA ARIMA-Backward Aandelen

*The author of this computation has been verified*

R Software Module: /rwasp_arimabackwardselection.wasp (opens new window with default values)

Title produced by software: ARIMA Backward Selection

Date of computation: Wed, 15 Dec 2010 18:21:11 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437192sfr4n2hwgkg4ijn.htm/, Retrieved Wed, 15 Dec 2010 19:19:59 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437192sfr4n2hwgkg4ijn.htm/}, year = {2010}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2010}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

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Paper DMA

Dataseries X:

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3030,29 2803,47 2767,63 2882,6 2863,36 2897,06 3012,61 3142,95 3032,93 3045,78 3110,52 3013,24 2987,1 2995,55 2833,18 2848,96 2794,83 2845,26 2915,03 2892,63 2604,42 2641,65 2659,81 2638,53 2720,25 2745,88 2735,7 2811,7 2799,43 2555,28 2304,98 2214,95 2065,81 1940,49 2042 1995,37 1946,81 1765,9 1635,25 1833,42 1910,43 1959,67 1969,6 2061,41 2093,48 2120,88 2174,56 2196,72 2350,44 2440,25 2408,64 2472,81 2407,6 2454,62 2448,05 2497,84 2645,64 2756,76 2849,27 2921,44 2981,85 3080,58 3106,22 3119,31 3061,26 3097,31 3161,69 3257,16 3277,01 3295,32 3363,99 3494,17 3667,03 3813,06 3917,96 3895,51 3801,06 3570,12 3701,61 3862,27 3970,1 4138,52 4199,75 4290,89 4443,91 4502,64 4356,98 4591,27 4696,96 4621,4 4562,84 4202,52 4296,49 4435,23 4105,18 4116,68 3844,49 3720,98 3674,4 3857,62 3801,06 3504,37 3032,6 3047,03 2962,34 2197,82 2014,45 1862,83 1905,41

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 20 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 ARIMA Parameter Estimation and Backward Selection Iteration ar1 ar2 ar3 ma1 sar1 sar2 sma1 Estimates ( 1 ) 0.9818 -0.244 0.1833 -0.7517 -0.3675 -0.1264 0.3495 (p-val) (0 ) (0.0782 ) (0.0886 ) (0 ) (0.5645 ) (0.359 ) (0.5784 ) Estimates ( 2 ) 0.9711 -0.241 0.1863 -0.7441 -0.0201 -0.1111 0 (p-val) (0 ) (0.0812 ) (0.0844 ) (0 ) (0.8672 ) (0.4199 ) (NA ) Estimates ( 3 ) 0.9716 -0.2412 0.1852 -0.7458 0 -0.1122 0 (p-val) (0 ) (0.0811 ) (0.0851 ) (0 ) (NA ) (0.415 ) (NA ) Estimates ( 4 ) 0.9733 -0.2361 0.1811 -0.7437 0 0 0 (p-val) (0 ) (0.0882 ) (0.0941 ) (0 ) (NA ) (NA ) (NA ) Estimates ( 5 ) -0.557 0.1671 0 0.8843 0 0 0 (p-val) (4e-04 ) (0.1479 ) (NA ) (0 ) (NA ) (NA ) (NA ) Estimates ( 6 ) -0.4521 0 0 0.7293 0 0 0 (p-val) (0.1514 ) (NA ) (NA ) (0.0052 ) (NA ) (NA ) (NA ) Estimates ( 7 ) 0 0 0 0.3034 0 0 0 (p-val) (NA ) (NA ) (NA ) (0.0028 ) (NA ) (NA ) (NA ) Estimates ( 8 ) NA NA NA NA NA NA NA (p-val) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) Estimates ( 9 ) NA NA NA NA NA NA NA (p-val) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) Estimates ( 10 ) NA NA NA NA NA NA NA (p-val) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) Estimates ( 11 ) NA NA NA NA NA NA NA (p-val) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) Estimates ( 12 ) NA NA NA NA NA NA NA (p-val) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) Estimates ( 13 ) NA NA NA NA NA NA NA (p-val) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) Estimated ARIMA Residuals Value 3.03028833849435 -216.600133786244 12.1887666299580 89.0269221038321 -31.241720802397 47.4931280790963 96.095157145235 112.511538158024 -133.013734861598 60.0581843288065 26.7565930948723 -87.5181319920062 -6.29431655241194 1.22340117339074 -159.440570174976 58.6564606247865 -89.7736739652246 91.4309583188638 25.8875189296997 -9.73946292783467 -291.233115317472 119.336265723966 -52.0408245670173 24.8823071953864 53.9537503053362 23.2241367414704 -15.5309301102941 82.7246304332868 -38.2439983095661 -221.805717404737 -198.908827724145 -58.1174947644814 -147.454151757873 -85.2028016883987 106.995820169963 -78.772782922104 -12.1911150325275 -193.971045081145 -70.9702915418206 190.866700682729 27.3967809140098 64.0727219013649 -14.5383815703952 106.901654629954 -4.38906893379470 45.0984035765489 33.1764903186612 22.2311204716346 147.524627775312 51.7118285907917 -28.7237016845274 70.828412177701 -87.8560283239944 81.6139876053944 -44.8346494758011 79.5175188918042 112.316487744441 96.0226514601923 72.7141330316326 60.9600476626852 48.5773501166182 90.611749699317 4.18926334565685 21.6255656185231 -67.9039098629587 59.3298064402329 37.4079456727541 97.2921730533517 -7.94642230089039 33.0786062254106 52.823223983818 122.699266073864 142.22531975243 120.448955310123 83.0715680483731 -35.612548360496 -78.62676006133 -216.295009801833 184.833941788802 85.3032113438803 118.246672705795 130.929068527740 41.8800813097187 88.2766996899782 129.841077658647 33.2118547150476 -143.331778862304 272.973946893810 12.5249725718595 -36.9163753127887 -65.7946768653301 -338.808989156156 178.175140165751 51.2782134788658 -304.728284168654 84.5341524930191 -328.641392735516 -6.88015431109216 -97.396012932296 233.19325516244 -143.799887819531 -217.386319778725 -447.352971818506 127.413531152613 -171.088439027969 -678.031389986494 -34.4945159417234 -209.357264642499 126.721522309825

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437192sfr4n2hwgkg4ijn/1cclc1292437251.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437192sfr4n2hwgkg4ijn/1cclc1292437251.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437192sfr4n2hwgkg4ijn/2442x1292437251.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437192sfr4n2hwgkg4ijn/2442x1292437251.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437192sfr4n2hwgkg4ijn/3442x1292437251.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437192sfr4n2hwgkg4ijn/3442x1292437251.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437192sfr4n2hwgkg4ijn/4442x1292437251.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437192sfr4n2hwgkg4ijn/4442x1292437251.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437192sfr4n2hwgkg4ijn/5fvki1292437251.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437192sfr4n2hwgkg4ijn/5fvki1292437251.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437192sfr4n2hwgkg4ijn/6fvki1292437251.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437192sfr4n2hwgkg4ijn/6fvki1292437251.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437192sfr4n2hwgkg4ijn/7fvki1292437251.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/15/t1292437192sfr4n2hwgkg4ijn/7fvki1292437251.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

R code (references can be found in the software module):

library(lattice) if (par1 == 'TRUE') par1 <- TRUE if (par1 == 'FALSE') par1 <- FALSE par2 <- as.numeric(par2) #Box-Cox lambda transformation parameter par3 <- as.numeric(par3) #degree of non-seasonal differencing par4 <- as.numeric(par4) #degree of seasonal differencing par5 <- as.numeric(par5) #seasonal period par6 <- as.numeric(par6) #degree (p) of the non-seasonal AR(p) polynomial par7 <- as.numeric(par7) #degree (q) of the non-seasonal MA(q) polynomial par8 <- as.numeric(par8) #degree (P) of the seasonal AR(P) polynomial par9 <- as.numeric(par9) #degree (Q) of the seasonal MA(Q) polynomial armaGR <- function(arima.out, names, n){ try1 <- arima.out$coef try2 <- sqrt(diag(arima.out$var.coef)) try.data.frame <- data.frame(matrix(NA,ncol=4,nrow=length(names))) dimnames(try.data.frame) <- list(names,c('coef','std','tstat','pv')) try.data.frame[,1] <- try1 for(i in 1:length(try2)) try.data.frame[which(rownames(try.data.frame)==names(try2)[i]),2] <- try2[i] try.data.frame[,3] <- try.data.frame[,1] / try.data.frame[,2] try.data.frame[,4] <- round((1-pt(abs(try.data.frame[,3]),df=n-(length(try2)+1)))*2,5) vector <- rep(NA,length(names)) vector[is.na(try.data.frame[,4])] <- 0 maxi <- which.max(try.data.frame[,4]) continue <- max(try.data.frame[,4],na.rm=TRUE) > .05 vector[maxi] <- 0 list(summary=try.data.frame,next.vector=vector,continue=continue) } arimaSelect <- function(series, order=c(13,0,0), seasonal=list(order=c(2,0,0),period=12), include.mean=F){ nrc <- order[1]+order[3]+seasonal$order[1]+seasonal$order[3] coeff <- matrix(NA, nrow=nrc*2, ncol=nrc) pval <- matrix(NA, nrow=nrc*2, ncol=nrc) mylist <- rep(list(NULL), nrc) names <- NULL if(order[1] > 0) names <- paste('ar',1:order[1],sep='') if(order[3] > 0) names <- c( names , paste('ma',1:order[3],sep='') ) if(seasonal$order[1] > 0) names <- c(names, paste('sar',1:seasonal$order[1],sep='')) if(seasonal$order[3] > 0) names <- c(names, paste('sma',1:seasonal$order[3],sep='')) arima.out <- arima(series, order=order, seasonal=seasonal, include.mean=include.mean, method='ML') mylist[[1]] <- arima.out last.arma <- armaGR(arima.out, names, length(series)) mystop <- FALSE i <- 1 coeff[i,] <- last.arma[[1]][,1] pval [i,] <- last.arma[[1]][,4] i <- 2 aic <- arima.out$aic while(!mystop){ mylist[[i]] <- arima.out arima.out <- arima(series, order=order, seasonal=seasonal, include.mean=include.mean, method='ML', fixed=last.arma$next.vector) aic <- c(aic, arima.out$aic) last.arma <- armaGR(arima.out, names, length(series)) mystop <- !last.arma$continue coeff[i,] <- last.arma[[1]][,1] pval [i,] <- last.arma[[1]][,4] i <- i+1 } list(coeff, pval, mylist, aic=aic) } arimaSelectplot <- function(arimaSelect.out,noms,choix){ noms <- names(arimaSelect.out[[3]][[1]]$coef) coeff <- arimaSelect.out[[1]] k <- min(which(is.na(coeff[,1])))-1 coeff <- coeff[1:k,] pval <- arimaSelect.out[[2]][1:k,] aic <- arimaSelect.out$aic[1:k] coeff[coeff==0] <- NA n <- ncol(coeff) if(missing(choix)) choix <- k layout(matrix(c(1,1,1,2, 3,3,3,2, 3,3,3,4, 5,6,7,7),nr=4), widths=c(10,35,45,15), heights=c(30,30,15,15)) couleurs <- rainbow(75)[1:50]#(50) ticks <- pretty(coeff) par(mar=c(1,1,3,1)) plot(aic,k:1-.5,type='o',pch=21,bg='blue',cex=2,axes=F,lty=2,xpd=NA) points(aic[choix],k-choix+.5,pch=21,cex=4,bg=2,xpd=NA) title('aic',line=2) par(mar=c(3,0,0,0)) plot(0,axes=F,xlab='',ylab='',xlim=range(ticks),ylim=c(.1,1)) rect(xleft = min(ticks) + (0:49)/50*(max(ticks)-min(ticks)), xright = min(ticks) + (1:50)/50*(max(ticks)-min(ticks)), ytop = rep(1,50), ybottom= rep(0,50),col=couleurs,border=NA) axis(1,ticks) rect(xleft=min(ticks),xright=max(ticks),ytop=1,ybottom=0) text(mean(coeff,na.rm=T),.5,'coefficients',cex=2,font=2) par(mar=c(1,1,3,1)) image(1:n,1:k,t(coeff[k:1,]),axes=F,col=couleurs,zlim=range(ticks)) for(i in 1:n) for(j in 1:k) if(!is.na(coeff[j,i])) { if(pval[j,i]<.01) symb = 'green' else if( (pval[j,i]<.05) & (pval[j,i]>=.01)) symb = 'orange' else if( (pval[j,i]<.1) & (pval[j,i]>=.05)) symb = 'red' else symb = 'black' polygon(c(i+.5 ,i+.2 ,i+.5 ,i+.5), c(k-j+0.5,k-j+0.5,k-j+0.8,k-j+0.5), col=symb) if(j==choix) { rect(xleft=i-.5, xright=i+.5, ybottom=k-j+1.5, ytop=k-j+.5, lwd=4) text(i, k-j+1, round(coeff[j,i],2), cex=1.2, font=2) } else{ rect(xleft=i-.5,xright=i+.5,ybottom=k-j+1.5,ytop=k-j+.5) text(i,k-j+1,round(coeff[j,i],2),cex=1.2,font=1) } } axis(3,1:n,noms) par(mar=c(0.5,0,0,0.5)) plot(0,axes=F,xlab='',ylab='',type='n',xlim=c(0,8),ylim=c(-.2,.8)) cols <- c('green','orange','red','black') niv <- c('0','0.01','0.05','0.1') for(i in 0:3){ polygon(c(1+2*i ,1+2*i ,1+2*i-.5 ,1+2*i), c(.4 ,.7 , .4 , .4), col=cols[i+1]) text(2*i,0.5,niv[i+1],cex=1.5) } text(8,.5,1,cex=1.5) text(4,0,'p-value',cex=2) box() residus <- arimaSelect.out[[3]][[choix]]$res par(mar=c(1,2,4,1)) acf(residus,main='') title('acf',line=.5) par(mar=c(1,2,4,1)) pacf(residus,main='') title('pacf',line=.5) par(mar=c(2,2,4,1)) qqnorm(residus,main='') title('qq-norm',line=.5) qqline(residus) residus } if (par2 == 0) x <- log(x) if (par2 != 0) x <- x^par2 (selection <- arimaSelect(x, order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5))) bitmap(file='test1.png') resid <- arimaSelectplot(selection) dev.off() resid bitmap(file='test2.png') acf(resid,length(resid)/2, main='Residual Autocorrelation Function') dev.off() bitmap(file='test3.png') pacf(resid,length(resid)/2, main='Residual Partial Autocorrelation Function') dev.off() bitmap(file='test4.png') cpgram(resid, main='Residual Cumulative Periodogram') dev.off() bitmap(file='test5.png') hist(resid, main='Residual Histogram', xlab='values of Residuals') dev.off() bitmap(file='test6.png') densityplot(~resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test7.png') qqnorm(resid, main='Residual Normal Q-Q Plot') qqline(resid) dev.off() ncols <- length(selection[[1]][1,]) nrows <- length(selection[[2]][,1])-1 load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'ARIMA Parameter Estimation and Backward Selection', ncols+1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Iteration', header=TRUE) for (i in 1:ncols) { a<-table.element(a,names(selection[[3]][[1]]$coef)[i],header=TRUE) } a<-table.row.end(a) for (j in 1:nrows) { a<-table.row.start(a) mydum <- 'Estimates (' mydum <- paste(mydum,j) mydum <- paste(mydum,')') a<-table.element(a,mydum, header=TRUE) for (i in 1:ncols) { a<-table.element(a,round(selection[[1]][j,i],4)) } a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'(p-val)', header=TRUE) for (i in 1:ncols) { mydum <- '(' mydum <- paste(mydum,round(selection[[2]][j,i],4),sep='') mydum <- paste(mydum,')') a<-table.element(a,mydum) } a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated ARIMA Residuals', 1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Value', 1,TRUE) a<-table.row.end(a) for (i in (par4*par5+par3):length(resid)) { a<-table.row.start(a) a<-table.element(a,resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab')

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