Arima - Parameters selecteren

*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: Sun, 12 Dec 2010 13:50:49 +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/12/t1292161736mczkufn3g3z054r.htm/, Retrieved Sun, 12 Dec 2010 14:49:03 +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/12/t1292161736mczkufn3g3z054r.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:

» Textbox « » Textfile « » CSV «

43880 43110 44496 44164 40399 36763 37903 35532 35533 32110 33374 35462 33508 36080 34560 38737 38144 37594 36424 36843 37246 38661 40454 44928 48441 48140 45998 47369 49554 47510 44873 45344 42413 36912 43452 42142 44382 43636 44167 44423 42868 43908 42013 38846 35087 33026 34646 37135 37985 43121 43722 43630 42234 39351 39327 35704 30466 28155 29257 29998 32529 34787 33855 34556 31348 30805 28353 24514 21106 21346 23335 24379 26290 30084 29429 30632 27349 27264 27474 24482 21453 18788 19282 19713 21917 23812 23785 24696 24562 23580 24939 23899 21454 19761 19815 20780 23462 25005 24725 26198 27543 26471 26558 25317 22896 22248 23406 25073 27691 30599 31948 32946 34012 32936 32974 30951 29812 29010 31068 32447 34844 35676 35387 36488 35652 33488 32914 29781 27951

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 29 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 ) 0.4657 0.1734 0.0266 -0.5801 0.1316 -0.0113 -1 (p-val) (0.3705 ) (0.1378 ) (0.84 ) (0.2553 ) (0.243 ) (0.9219 ) (0 ) Estimates ( 2 ) 0.468 0.1727 0.0256 -0.5822 0.132 0 -1 (p-val) (0.3761 ) (0.1397 ) (0.8463 ) (0.2617 ) (0.2413 ) (NA ) (0 ) Estimates ( 3 ) 0.5371 0.1853 0 -0.6487 0.1297 0 -1.0001 (p-val) (0.1108 ) (0.0576 ) (NA ) (0.0494 ) (0.2472 ) (NA ) (0 ) Estimates ( 4 ) 0.614 0.1512 0 -0.6995 0 0 -0.9996 (p-val) (0.1533 ) (0.1116 ) (NA ) (0.1008 ) (NA ) (NA ) (8e-04 ) Estimates ( 5 ) 0 0.1046 0 -0.0832 0 0 -1.0006 (p-val) (NA ) (0.27 ) (NA ) (0.3778 ) (NA ) (NA ) (9e-04 ) Estimates ( 6 ) 0 0.0984 0 0 0 0 -1.0002 (p-val) (NA ) (0.2941 ) (NA ) (NA ) (NA ) (NA ) (2e-04 ) Estimates ( 7 ) 0 0 0 0 0 0 -1.0001 (p-val) (NA ) (NA ) (NA ) (NA ) (NA ) (NA ) (0 ) 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 -174.886022089202 2351.46555527189 -2044.73045654871 2955.35134262666 2444.72193754406 1868.05986875612 -1854.35805358801 1758.72046632912 443.644907460096 3237.54881409586 335.811261467436 1467.71088800452 3732.61637494243 -1134.03439050159 -2013.26066381157 -353.759046642968 3729.47987323017 84.2469628333906 -2491.50579275538 1177.76223316418 -2348.1888699199 -3782.95468989825 4334.63649664493 -3338.71715387341 704.973533972732 -735.468921701612 1013.46600256034 -1177.75650203666 -829.296324927534 2825.16013250752 -800.503302904596 -2580.41892622136 -2440.57615544506 613.080946564223 -1123.98052010769 628.722605889011 -277.564724561049 4359.67324546163 966.65898726552 -1741.21539979488 -506.331024813696 -1289.51629087126 1039.26224959993 -2061.12215679824 -3377.83435803007 293.555707434045 -1203.28938530775 -1033.11073957741 1338.82995635458 1084.30343610524 -756.3966126222 -439.328945161693 -1929.68567724349 1011.80721779575 -1204.93208091783 -2090.23265235321 -869.50482348231 2587.93141413073 -337.428317983055 -792.791369652984 445.342168975662 2308.7123253455 -325.086558270224 -46.5148321383592 -1725.54823489017 1233.39147915953 1452.79008243268 -1024.14400145782 -626.533412440235 -578.71692397227 -1703.75081020146 -967.693320801713 783.160382801778 277.26282410189 280.121749908975 -138.602359450726 1393.18084719073 256.034928286101 2042.99163206858 1021.39913602330 -102.117200489187 228.313004751229 -1940.73367752645 -427.676634963762 1166.43871407722 -137.477910874454 -34.3340969487134 440.232267858213 2646.43160992191 88.8172820639761 465.39050831349 719.649417298171 50.5769879765941 1205.12511692484 -673.015508905243 187.479886645266 866.019546335448 1106.66116247926 1521.41284822681 -184.254338915451 1950.31030524183 119.990408212145 395.824167214157 -97.7438862665265 1265.93169661807 1004.93590051821 132.268332186196 -89.9187016152298 482.653494930743 -951.18248623997 -164.302949582457 126.310341135538 104.481441227983 -938.403022036979 -46.9787218860189 -1044.58951980807 543.713582309755

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/12/t1292161736mczkufn3g3z054r/1c3g11292161819.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292161736mczkufn3g3z054r/1c3g11292161819.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292161736mczkufn3g3z054r/2c3g11292161819.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292161736mczkufn3g3z054r/2c3g11292161819.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292161736mczkufn3g3z054r/3c3g11292161819.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292161736mczkufn3g3z054r/3c3g11292161819.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292161736mczkufn3g3z054r/4c3g11292161819.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292161736mczkufn3g3z054r/4c3g11292161819.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292161736mczkufn3g3z054r/55cxm1292161819.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292161736mczkufn3g3z054r/55cxm1292161819.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292161736mczkufn3g3z054r/65cxm1292161819.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292161736mczkufn3g3z054r/65cxm1292161819.ps (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292161736mczkufn3g3z054r/75cxm1292161819.png (open in new window) http://www.freestatistics.org/blog/date/2010/Dec/12/t1292161736mczkufn3g3z054r/75cxm1292161819.ps (open in new window)

Parameters (Session):

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

Parameters (R input):

par1 = FALSE ; par2 = 1 ; par3 = 1 ; 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

Disclaimer

Information provided on this web site is provided "AS IS" without warranty of any kind, either express or implied, including, without limitation, warranties of merchantability, fitness for a particular purpose, and noninfringement. We use reasonable efforts to include accurate and timely information and periodically update the information, and software without notice. However, we make no warranties or representations as to the accuracy or completeness of such information (or software), and we assume no liability or responsibility for errors or omissions in the content of this web site, or any software bugs in online applications. Your use of this web site is AT YOUR OWN RISK. Under no circumstances and under no legal theory shall we be liable to you or any other person for any direct, indirect, special, incidental, exemplary, or consequential damages arising from your access to, or use of, this web site.

Privacy Policy

We may request personal information to be submitted to our servers in order to be able to:

• personalize online software applications according to your needs
• enforce strict security rules with respect to the data that you upload (e.g. statistical data)
• manage user sessions of online applications
• alert you about important changes or upgrades in resources or applications

We NEVER allow other companies to directly offer registered users information about their products and services. Banner references and hyperlinks of third parties NEVER contain any personal data of the visitor.

We do NOT sell, nor transmit by any means, personal information, nor statistical data series uploaded by you to third parties.

We carefully protect your data from loss, misuse, alteration, and destruction. However, at any time, and under any circumstance you are solely responsible for managing your passwords, and keeping them secret.

We store a unique ANONYMOUS USER ID in the form of a small 'Cookie' on your computer. This allows us to track your progress when using this website which is necessary to create state-dependent features. The cookie is used for NO OTHER PURPOSE. At any time you may opt to disallow cookies from this website - this will not affect other features of this website.

We examine cookies that are used by third-parties (banner and online ads) very closely: abuse from third-parties automatically results in termination of the advertising contract without refund. We have very good reason to believe that the cookies that are produced by third parties (banner ads) do NOT cause any privacy or security risk.

FreeStatistics.org is safe. There is no need to download any software to use the applications and services contained in this website. Hence, your system's security is not compromised by their use, and your personal data - other than data you submit in the account application form, and the user-agent information that is transmitted by your browser - is never transmitted to our servers.

As a general rule, we do not log on-line behavior of individuals (other than normal logging of webserver 'hits'). However, in cases of abuse, hacking, unauthorized access, Denial of Service attacks, illegal copying, hotlinking, non-compliance with international webstandards (such as robots.txt), or any other harmful behavior, our system engineers are empowered to log, track, identify, publish, and ban misbehaving individuals - even if this leads to ban entire blocks of IP addresses, or disclosing user's identity.

FreeStatistics.org is powered by