arima backward selection: goudprijs

*Unverified author*

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

Title produced by software: ARIMA Backward Selection

Date of computation: Wed, 30 Dec 2009 06:34:07 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/30/t1262180099mbte92hqg7l8lgj.htm/, Retrieved Wed, 30 Dec 2009 14:35:08 +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/2009/Dec/30/t1262180099mbte92hqg7l8lgj.htm/}, year = {2009}, } @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 = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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10070 10137 9984 9732 9103 9155 9308 9394 9948 10177 10002 9728 10002 10063 10018 9960 10236 10893 10756 10940 10997 10827 10166 10186 10457 10368 10244 10511 10812 10738 10171 9721 9897 9828 9924 10371 10846 10413 10709 10662 10570 10297 10635 10872 10296 10383 10431 10574 10653 10805 10872 10625 10407 10463 10556 10646 10702 11353 11346 11451 11964 12574 13031 13812 14544 14931 14886 16005 17064 15168 16050 15839 15137 14954 15648 15305 15579 16348 15928 16171 15937 15713 15594 15683 16438 17032 17696 17745 19394 20148 20108 18584 18441 18391 19178 18079 18483 19644 19195 19650 20830 23595 22937 21814 21928 21777 21383 21467 22052 22680 24320

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 7 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 ) 0.2895 -0.1524 0.1319 -0.2209 0.4694 0.135 -0.3409 (p-val) (0.4641 ) (0.1704 ) (0.2197 ) (0.5697 ) (0.3897 ) (0.4506 ) (0.536 ) Estimates ( 2 ) 0.07 -0.1414 0.0899 0 0.4835 0.1354 -0.3582 (p-val) (0.5104 ) (0.1796 ) (0.3607 ) (NA ) (0.3505 ) (0.4439 ) (0.4926 ) Estimates ( 3 ) 0 -0.1357 0.0798 0 0.4855 0.134 -0.3321 (p-val) (NA ) (0.1962 ) (0.4129 ) (NA ) (0.3582 ) (0.4775 ) (0.5335 ) Estimates ( 4 ) 0 -0.13 0.0875 0 0.1657 0.1926 0 (p-val) (NA ) (0.2132 ) (0.3675 ) (NA ) (0.121 ) (0.1333 ) (NA ) Estimates ( 5 ) 0 -0.1301 0 0 0.1619 0.1985 0 (p-val) (NA ) (0.2125 ) (NA ) (NA ) (0.1253 ) (0.1161 ) (NA ) Estimates ( 6 ) 0 0 0 0 0.1809 0.1423 0 (p-val) (NA ) (NA ) (NA ) (NA ) (0.0904 ) (0.2381 ) (NA ) Estimates ( 7 ) 0 0 0 0 0.1905 0 0 (p-val) (NA ) (NA ) (NA ) (NA ) (0.0845 ) (NA ) (NA ) Estimates ( 8 ) 0 0 0 0 0 0 0 (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 10.0699947754242 65.7731821094984 -150.198460641018 -247.385699879324 -617.482560413075 51.0478428322415 150.198460641018 84.4252785302456 543.855864020419 224.806846318910 -171.795624916197 -268.982864154503 268.980915214612 48.2372215011231 -15.8551476059929 -9.99671370398755 395.817726508698 647.094559970665 -166.144852394007 167.617926105329 -48.5310341586937 -213.622033975345 -627.664384516658 72.1940493853472 218.805950614653 -100.619843111337 -115.427984589998 278.048375417337 248.424972151986 -199.151424986032 -540.902975307326 -485.050018565342 165.142113813998 -36.6168306733252 221.913381911367 443.190215373332 423.377418308653 -416.046458411329 319.620664685339 -97.8606247660136 -149.337258631349 -258.90379688133 446.007394166028 322.720154100021 -609.526104714676 100.143756962003 29.7130337919953 57.8513135939775 -11.4823848833566 234.481837167355 10.6151875253181 -238.047006127332 -200.474990717328 108.003560154013 28.6146398093169 44.8540521739887 165.721797248028 634.427436873995 -16.1434831040024 77.760039919327 497.951350724663 581.045636837325 444.237221500664 828.050840139345 773.526652430677 376.33260304533 -62.7154985140041 1101.85596917999 1048.33260304533 -2020.00848959803 883.333424619334 -231.001369290005 -799.720975674025 -299.198431113364 606.946421280643 -491.772089671373 134.561882663964 695.28066747398 -411.427984589998 29.8425501379443 -435.728095982053 137.167582608094 -287.011502036044 129.193227811344 888.723440396036 628.859529334008 531.800473454634 114.337806347350 1596.80595061465 607.51378110463 40.0054771600226 -1570.28888321401 -98.4255198679894 -7.33041218132348 809.668218528674 -1115.95354158867 260.180630343297 1047.84939658797 -575.484849605367 445.666027664665 865.883257531252 2621.37111957463 -650.380430746663 -832.694411447923 141.239960080675 -141.475538433329 -543.915025059374 293.347665235389 508.042350541313 406.842002421941 1725.52966486869

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/30/t1262180099mbte92hqg7l8lgj/10qh11262180038.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262180099mbte92hqg7l8lgj/10qh11262180038.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262180099mbte92hqg7l8lgj/2jlxm1262180038.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262180099mbte92hqg7l8lgj/2jlxm1262180038.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262180099mbte92hqg7l8lgj/3he6g1262180038.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262180099mbte92hqg7l8lgj/3he6g1262180038.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262180099mbte92hqg7l8lgj/4in591262180038.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262180099mbte92hqg7l8lgj/4in591262180038.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262180099mbte92hqg7l8lgj/5i9b41262180038.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262180099mbte92hqg7l8lgj/5i9b41262180038.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262180099mbte92hqg7l8lgj/657cv1262180038.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262180099mbte92hqg7l8lgj/657cv1262180038.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262180099mbte92hqg7l8lgj/7uk251262180038.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/30/t1262180099mbte92hqg7l8lgj/7uk251262180038.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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Software written by Ed van Stee & Patrick Wessa

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