*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: Mon, 27 Dec 2010 20:26:52 +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/27/t1293481774bhu7ociefbcongd.htm/, Retrieved Mon, 27 Dec 2010 21:29:41 +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/27/t1293481774bhu7ociefbcongd.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}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

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60178 53200 59909 55970 47682 50173 43090 36031 42143 48478 36046 31060 54874 60051 71622 66526 50140 55973 40393 38483 42879 47875 40578 31027 62027 56493 65566 62653 53470 59600 42542 42018 44038 44988 43309 26843 69770 64886 79354 63025 54003 55926 45629 40361 43039 44570 43269 25563 68707 60223 74283 61232 61531 65305 51699 44599 35221 55066 45335 28702 69517 69240 71525 77740 62107 65450 51493 43067 49172 54483 38158 27898 58648 56000 62381 59849 48345 55376 45400 38389 44098 48290 41267 31238

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 'George Udny Yule' @ 72.249.76.132 ARIMA Parameter Estimation and Backward Selection Iteration ar1 ar2 ar3 ma1 sar1 sar2 sma1 Estimates ( 1 ) -0.1743 0.2261 0.1631 0.222 0.2444 -0.0786 -1 (p-val) (0.807 ) (0.0851 ) (0.3332 ) (0.7615 ) (0.1592 ) (0.6347 ) (0 ) Estimates ( 2 ) 0 0.2139 0.133 0.042 0.2401 -0.0766 -1 (p-val) (NA ) (0.0755 ) (0.3238 ) (0.7561 ) (0.1615 ) (0.6429 ) (0 ) Estimates ( 3 ) 0 0.215 0.1393 0 0.2287 -0.0595 -1.0001 (p-val) (NA ) (0.0732 ) (0.292 ) (NA ) (0.1712 ) (0.7047 ) (0 ) Estimates ( 4 ) 0 0.2151 0.1386 0 0.2445 0 -1 (p-val) (NA ) (0.0719 ) (0.2865 ) (NA ) (0.1303 ) (NA ) (0 ) Estimates ( 5 ) 0 0.2139 0 0 0.3175 0 -1.0001 (p-val) (NA ) (0.0755 ) (NA ) (NA ) (0.0351 ) (NA ) (0 ) Estimates ( 6 ) 0 0 0 0 0.3459 0 -1.0001 (p-val) (NA ) (NA ) (NA ) (NA ) (0.0242 ) (NA ) (0 ) Estimates ( 7 ) NA NA NA NA NA NA NA (p-val) (NA ) (NA ) (NA ) (NA ) (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 2.30811325595510e-11 1.00956903901927e-09 -1.36427282522118e-09 -1.82644350227369e-09 -1.45341826532962e-09 -3.96168279485338e-10 -1.03291531337273e-09 1.40873995029049e-09 -1.24461149831137e-09 -5.74784662981084e-10 4.97851101790116e-10 -2.51775255730836e-09 -1.03911774320232e-10 -5.26590556030447e-10 2.17041255987676e-10 4.21937714388022e-10 -9.3744749092248e-11 -1.2249384417269e-09 -1.24195310902139e-09 -3.68160563439152e-10 -2.2158098170076e-09 -4.88036042788066e-10 1.65069258877255e-09 -2.12609488068495e-09 5.28788897809202e-09 -1.02410154761328e-09 -2.78108885208995e-09 -1.38770259528902e-09 5.71508994197832e-11 -3.83426811729603e-10 1.1763176257295e-10 -1.3216962005033e-09 -4.23909067673618e-10 4.55238105131695e-10 7.73150196322664e-10 -1.33233210015745e-09 4.55172362118769e-09 -4.28109806873962e-10 -9.99242607371898e-10 -2.12386908009282e-10 1.02248140912670e-10 -2.12270165869481e-09 -2.02271026607816e-09 -2.38998142614597e-09 -2.29507418409573e-09 5.48461634738673e-09 -2.35622477319475e-09 -3.02673376535649e-09 -1.53091059598434e-09 -3.27286480318018e-10 -1.28088904373548e-09 1.25458571602598e-11 -1.89336515120727e-09 -1.40264533007525e-09 -6.48573435366508e-10 -1.37074213510054e-09 -6.70354891711273e-10 -4.57745666011735e-09 -1.03023446177505e-09 3.49492518642573e-09 1.3287522833497e-09 7.10759028739159e-10 1.13960209524076e-09 8.74827604106429e-10 1.00917365503492e-09 2.07691107959474e-09 7.45961546151894e-10 2.14546684983411e-10 1.43743525159065e-09 -1.50296049051229e-11 4.29520049469881e-10 -1.03816868802248e-09 -4.15826187675574e-09

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/27/t1293481774bhu7ociefbcongd/13x8w1293481592.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293481774bhu7ociefbcongd/13x8w1293481592.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293481774bhu7ociefbcongd/2e67z1293481592.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293481774bhu7ociefbcongd/2e67z1293481592.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293481774bhu7ociefbcongd/3e67z1293481592.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293481774bhu7ociefbcongd/3e67z1293481592.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293481774bhu7ociefbcongd/4e67z1293481592.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293481774bhu7ociefbcongd/4e67z1293481592.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293481774bhu7ociefbcongd/5e67z1293481592.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293481774bhu7ociefbcongd/5e67z1293481592.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293481774bhu7ociefbcongd/6ofo21293481592.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293481774bhu7ociefbcongd/6ofo21293481592.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293481774bhu7ociefbcongd/7ofo21293481592.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/27/t1293481774bhu7ociefbcongd/7ofo21293481592.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = -1.7 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = FALSE ; par2 = -1.7 ; par3 = 0 ; par4 = 1 ; 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')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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