Paper-ARIMAbackw-Yt

*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: Tue, 15 Dec 2009 11:35:49 -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/15/t1260902218jn12y9sbi5j1jf3.htm/, Retrieved Tue, 15 Dec 2009 19:37:08 +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/15/t1260902218jn12y9sbi5j1jf3.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:

SDHW, DSHW

Dataseries X:

» Textbox « » Textfile « » CSV «

128 502 629.7 595.9 823.7 498.7 766.9 1611.3 329.7 1378.9 1159.4 790.1 -189.6 862.4 426.6 852 834.7 1026.7 1052.8 1280.9 -243.6 976 908.2 416 610.7 728 520.8 905.8 768.9 479.3 1054.2 1411.9 -131 1526.2 1049.5 550.8 168.5 458.2 297 616.3 762.7 693.1 512.7 1169.2 -915.1 1384.2 1368.9 -275.1 -408.9 -37.5 171.5 671.8 -18.5 231.6 747.5 1505.7 -83.6 1173.2 1452.1 777 -52.8 861.2 735.2 1073.6 966.9 1189.8 1093.5 1782.7 -70.4 1471.6 1273.8 900.8 -910.2 299.8 460.2 677.2 937.1 1265.4 1275.6 1582.6 -154.2 1667.7 1083.1 891.7 -26.5 423.4 662.8 711.4 993.3 1133.2 343.9 1415.8 -531.8 1193.6 1201.3 805.6 -164.8

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 12 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 ) -0.3003 0.2621 0.2424 0.5547 0.1525 0.1486 -1 (p-val) (0.3714 ) (0.0694 ) (0.0307 ) (0.104 ) (0.2556 ) (0.2897 ) (0.0028 ) Estimates ( 2 ) 0 0.1822 0.1995 0.2492 0.136 0.1275 -0.9999 (p-val) (NA ) (0.0918 ) (0.0645 ) (0.0262 ) (0.3009 ) (0.3472 ) (0.0053 ) Estimates ( 3 ) 0 0.1782 0.1898 0.2467 0.0559 0 -0.8116 (p-val) (NA ) (0.1009 ) (0.0869 ) (0.0273 ) (0.7755 ) (NA ) (0.0034 ) Estimates ( 4 ) 0 0.1751 0.1989 0.2454 0 0 -0.7552 (p-val) (NA ) (0.1043 ) (0.0612 ) (0.028 ) (NA ) (NA ) (0 ) Estimates ( 5 ) 0 0 0.2105 0.2133 0 0 -0.7746 (p-val) (NA ) (NA ) (0.0547 ) (0.0279 ) (NA ) (NA ) (0 ) Estimates ( 6 ) 0 0 0 0.2421 0 0 -0.8333 (p-val) (NA ) (NA ) (NA ) (0.0165 ) (NA ) (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 0.790098685760698 -240.286776919260 328.591811860112 -213.635876932857 298.457994577103 -113.615925692757 473.145463405171 77.4372152539838 -273.753162261419 -493.691709801928 -287.176634354493 -55.7290037608449 -246.999614512969 688.338508855857 -78.5266784100142 71.8890910158688 22.6063222701892 -66.3498228167505 -249.238981173394 146.496067837964 -42.4452033659016 -87.1260123449437 317.39931966006 -27.8801552718772 -15.9787636083003 -93.3727851559264 -218.574620322313 -156.954932698832 -127.881676108871 34.2690911282097 65.2513815299818 -408.118699611051 -150.154403903611 -819.302516241956 345.582495219391 301.515656151425 -710.719206213384 -450.654877576726 -617.054918157008 26.5610562181256 50.9341672625952 -663.625979709982 -229.554420346569 -16.6469346749634 319.86138203698 224.907314990613 -182.781514931011 314.627721060879 319.636925277973 -117.528571240253 365.812781148711 183.202451634886 324.296599044965 230.914652987281 501.866375342385 101.494503156155 281.265536238965 -28.2772472728003 127.924820948259 -54.5614951194853 417.606688473757 -1036.60939906537 -40.6019157853152 -90.7097605829532 79.5489787704607 296.927377001688 484.620406903424 316.547667114668 -31.0220971002515 -68.5794563985398 260.958359821794 -223.965982053063 360.739995021891 38.2771501009297 -45.0885708420886 137.615815726068 -134.319302164646 298.086617829280 180.572353284010 -651.709666946478 -10.8084715004994 -402.734049642139 -2.50947226402265 24.5095731091008 227.242822745546 1.25190834832096

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/15/t1260902218jn12y9sbi5j1jf3/10h2j1260902136.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260902218jn12y9sbi5j1jf3/10h2j1260902136.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260902218jn12y9sbi5j1jf3/2m8xg1260902136.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260902218jn12y9sbi5j1jf3/2m8xg1260902136.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260902218jn12y9sbi5j1jf3/3b5pg1260902136.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260902218jn12y9sbi5j1jf3/3b5pg1260902136.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260902218jn12y9sbi5j1jf3/4uqyl1260902136.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260902218jn12y9sbi5j1jf3/4uqyl1260902136.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260902218jn12y9sbi5j1jf3/5ao6j1260902136.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260902218jn12y9sbi5j1jf3/5ao6j1260902136.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260902218jn12y9sbi5j1jf3/6nivs1260902136.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260902218jn12y9sbi5j1jf3/6nivs1260902136.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260902218jn12y9sbi5j1jf3/7wlla1260902136.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/15/t1260902218jn12y9sbi5j1jf3/7wlla1260902136.ps (open in new window)

Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 12 ;

Parameters (R input):

par1 = FALSE ; par2 = 1 ; 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')

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