*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, 14 Dec 2010 15:33:03 +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/14/t1292340660i7d16r3s6jcjr4i.htm/, Retrieved Tue, 14 Dec 2010 16:33:10 +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/14/t1292340660i7d16r3s6jcjr4i.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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1145.11 1176.86 1206.41 1192.72 1214.82 1199.07 1157.47 1100.1 1095.63 1105.63 1137.79 1124.72 1152.6 1211.85 1239.62 1244.13 1198.42 1227.99 1304.92 1340.26 1307.32 1356.51 1383.29 1437.87 1494.56 1521.42 1498.76 1488.75 1524.62 1439.27 1423.11 1466.85 1425.83 1363.45 1389.18 1395.89 1368.43 1349.03 1299.88 1365.41 1451.04 1433.75 1464.65 1475.57 1471.16 1429.12 1452.46 1538.09 1631.59 1665.5 1690.6 1711.74 1734.1 1748.09 1703.45 1745.74 1751.01 1795.65 1852.13 1877.1 1989.31 2097.76 2154.87 2152.18 2250.27 2346.9 2525.56 2409.36 2394.36 2401.33 2354.32 2450.41 2504.67 2661.39 2880.4 3064.42 3141.12 3327.7 3564.95 3403.13 3149.9 3006.84 3230.66 3361.13 3484.74 3411.13 3288.18 3280.37 3173.95 3165.26 3092.71 3053.05 3181.96 2999.93 3249.57 3210.52 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 2915.02 2 etc...

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 9 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 ) -0.4913 0.3829 0.4174 0.2935 0.1948 -0.471 0.2935 (p-val) (0.0186 ) (0 ) (0 ) (0.808 ) (0.2089 ) (0 ) (0.808 ) Estimates ( 2 ) -0.5886 0.4509 0.4135 0 0.1785 -0.4305 0.707 (p-val) (0.0013 ) (0 ) (0 ) (NA ) (0.1632 ) (0 ) (0.0063 ) Estimates ( 3 ) -0.5718 0.5029 0.319 0 0 -0.3465 0.8551 (p-val) (0 ) (0 ) (4e-04 ) (NA ) (NA ) (4e-04 ) (0 ) Estimates ( 4 ) NA NA NA NA NA NA NA (p-val) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) Estimates ( 5 ) NA NA NA NA NA NA NA (p-val) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) Estimates ( 6 ) NA NA NA NA NA NA NA (p-val) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) 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 1.14510934051474 29.5831519191089 19.877488750705 -21.0773250189315 23.2601215783404 -28.2180766336424 -39.0072041830626 -50.2705342734260 13.6433222105837 7.00796559363794 44.2330742870726 -17.7278907581283 40.9633800910056 40.3928917555035 15.4074887572086 -8.8039933848595 -46.8708733392805 29.0914821367792 59.9781355327506 18.9331045452236 -39.1476025921752 57.3706927041309 -6.80897993597703 48.8849886538227 34.901689756515 16.396695907082 -46.6792310267876 -5.5231479611548 19.8369657383799 -94.9237543148447 10.1893124083478 42.9969137998007 -47.1813347522284 -46.1646775246676 51.582935942008 -10.4938437145402 -18.3966974245396 -5.74297021644041 -42.1257666878921 74.3921106056191 69.7321153115764 -28.55562666021 37.3942486737373 -6.63536974001851 -19.7045551719977 -46.9143703249648 38.3111043348601 66.9289172724648 80.3084178078253 8.71349923214574 18.9633196796815 -8.1371792206055 4.4399844856639 -5.35552484742561 -48.662805603625 47.8382303781107 -13.1744664197395 48.7045829057433 39.1998065064747 17.2565981910534 91.4421190107085 75.8754114823905 17.1314938897995 -26.9921682228683 82.3159105527925 41.4256434429508 150.732233364553 -179.284912860423 22.6570839440115 -43.9463083213059 -40.6272199492732 88.0293563240757 59.2632168336145 130.595391564722 180.896633539073 118.763249884595 4.5955479266031 145.725292741571 132.204427252000 -248.637832764873 -230.435959544483 -118.699009050447 231.994996831003 73.6120609540522 167.658547809545 -113.379844176488 -100.347420936341 -43.4410732864271 -95.7073895430194 12.9632372671422 -43.4098288339701 -6.3227395644999 141.102881275581 -198.172687401915 312.354829668964 -127.254447499231 -131.536277150492 -223.791190918921 57.4624117335011 62.7347276658115 34.7671795456945 49.0256845529561 132.645655834529 73.8035824987219 -144.082816597475 43.4000544736723 22.8428831730043 -115.968061985014 -3.16234016280714 25.0502579329532 -175.654462318769 74.578496058326 -60.2232725323579 85.40941360748 53.6186713580992 -6.69648046838029 -301.729857195751 133.172448828607 -40.1422045540739 23.1279957908168 90.0480375982575 43.5288755721663 -47.8134077403024 95.2252006933773 -55.2332768561018 -236.487243644851 -191.089348288010 -33.2956347537156 -123.702915650186 -36.2225982616903 175.184857984655 -45.8547856841988 -4.04554827152742 -158.583296216273 -72.8162089447185 210.181528657962 54.6419202333277 58.1446859857674 11.4730954103736 74.8726516068173 -32.9235778410969 31.8855218756626 21.0709520610294 10.4715767544326 126.283725423292 47.5050374010816 -60.7542342093757 58.4141336410376 -105.820290420611 51.392634981165 -32.7388896769062 67.4484290206938 114.030403141996 91.3431354922036 43.4066313467552 48.8749573609512 8.3446958828872 61.497924893255 -21.5907602177031 -3.48374974071794 -81.4203528852245 43.4910756159616 33.9980285157672 91.8017870758004 -12.2005074939002 23.9613015460604 34.97542635321 106.790636991715 121.288494198168 103.625198316313 47.9371241993072 -73.3085253350491 -120.598800135265 -238.293626969748 180.281065207151 107.662815883300 114.869327083717 145.379211571178 26.4722584637875 25.0733669427573 109.991172897771 -12.0497494565843 -176.867744069596 258.167575110294 -1.78355845331316 -83.0451232641126 -55.7088432698911 -346.147267222352 149.877567942319 111.472252539601 -314.534133374292 127.383238927835 -274.341245231075 -49.7264073864894 -13.8344115667983 268.464417687361 -124.838486916581 -187.59369277682 -440.737459872609 160.544166579793 -135.236742261389 -622.084792331595 61.9433997319716 -85.6862983151102 132.555559881305 -29.9928368703957 6.45548746267627 191.346273053471 179.089969617082 -81.4858049865329 84.3707146368966 169.403196535344 60.8251686973995 26.444766474242 -73.7972539004536 14.1159884907506

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340660i7d16r3s6jcjr4i/1qfiv1292340773.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340660i7d16r3s6jcjr4i/1qfiv1292340773.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340660i7d16r3s6jcjr4i/2qfiv1292340773.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340660i7d16r3s6jcjr4i/2qfiv1292340773.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340660i7d16r3s6jcjr4i/3qfiv1292340773.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340660i7d16r3s6jcjr4i/3qfiv1292340773.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340660i7d16r3s6jcjr4i/4160g1292340773.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340660i7d16r3s6jcjr4i/4160g1292340773.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340660i7d16r3s6jcjr4i/5160g1292340773.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340660i7d16r3s6jcjr4i/5160g1292340773.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340660i7d16r3s6jcjr4i/6160g1292340773.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340660i7d16r3s6jcjr4i/6160g1292340773.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340660i7d16r3s6jcjr4i/7160g1292340773.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/14/t1292340660i7d16r3s6jcjr4i/7160g1292340773.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; 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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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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