tabel

*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, 01 Dec 2009 07:41:19 -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/01/t1259678606j51qcvwdd6kegr0.htm/, Retrieved Tue, 01 Dec 2009 15:43:41 +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/2009/Dec/01/t1259678606j51qcvwdd6kegr0.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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325412 326011 328282 317480 317539 313737 312276 309391 302950 300316 304035 333476 337698 335932 323931 313927 314485 313218 309664 302963 298989 298423 310631 329765 335083 327616 309119 295916 291413 291542 284678 276475 272566 264981 263290 296806 303598 286994 276427 266424 267153 268381 262522 255542 253158 243803 250741 280445 285257 270976 261076 255603 260376 263903 264291 263276 262572 256167 264221 293860 300713 287224

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 ) 0.5899 -0.0342 0.2558 -0.5655 -0.7733 -0.2803 0.3924 (p-val) (0.2659 ) (0.8483 ) (0.1529 ) (0.2855 ) (0.9001 ) (0.8962 ) (0.9506 ) Estimates ( 2 ) 0.5679 -0.0348 0.2553 -0.5441 -0.3867 -0.1428 0 (p-val) (0.1625 ) (0.8437 ) (0.1481 ) (0.1791 ) (0.034 ) (0.4925 ) (NA ) Estimates ( 3 ) 0.5408 0 0.2444 -0.5294 -0.3805 -0.1358 0 (p-val) (0.1521 ) (NA ) (0.152 ) (0.187 ) (0.0332 ) (0.506 ) (NA ) Estimates ( 4 ) 0.5013 0 0.279 -0.4979 -0.3316 0 0 (p-val) (0.1276 ) (NA ) (0.0764 ) (0.1525 ) (0.0357 ) (NA ) (NA ) Estimates ( 5 ) 0.0545 0 0.2872 0 -0.3183 0 0 (p-val) (0.705 ) (NA ) (0.0646 ) (NA ) (0.0463 ) (NA ) (NA ) Estimates ( 6 ) 0 0 0.2853 0 -0.2998 0 0 (p-val) (NA ) (NA ) (0.066 ) (NA ) (0.051 ) (NA ) (NA ) Estimates ( 7 ) 0 0 0 0 -0.2679 0 0 (p-val) (NA ) (NA ) (NA ) (NA ) (0.072 ) (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 -1065.28076055322 -2278.75083745204 -13750.7320730183 768.487940174182 480.329421548304 2441.84534097982 -2017.12122801278 -3677.24413007058 2376.07844077739 1991.57956111441 8177.8663887305 -9931.36901798728 1054.78346037674 -6334.48912633556 -10318.8992855633 -2985.24764365473 -4927.33781231944 2075.02534260383 -3870.63118024471 -2524.15412506803 725.810856004154 -6465.06532185037 -11625.1356478526 11621.1659938228 1767.57466477775 -10664.0704054107 6189.98081853049 2343.11555395316 3876.36005581636 1472.93269355467 118.383083333785 820.674136304355 1542.41090621852 -3650.11001150461 4906.01253028907 40.3638959194068 -1585.17421898316 -124.437694132677 2791.13055865956 5387.15230614261 5445.44402054302 2593.37824514089 6516.19939614798 6292.59289700375 2088.48664589605 2475.88763066489 3427.36476553255 -1086.08268469240 1510.63701057434 1414.23900224041

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/01/t1259678606j51qcvwdd6kegr0/1ywsf1259678467.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259678606j51qcvwdd6kegr0/1ywsf1259678467.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259678606j51qcvwdd6kegr0/2eh1z1259678467.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259678606j51qcvwdd6kegr0/2eh1z1259678467.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259678606j51qcvwdd6kegr0/36r7g1259678467.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259678606j51qcvwdd6kegr0/36r7g1259678467.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259678606j51qcvwdd6kegr0/45st31259678467.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259678606j51qcvwdd6kegr0/45st31259678467.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259678606j51qcvwdd6kegr0/5s89k1259678467.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259678606j51qcvwdd6kegr0/5s89k1259678467.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259678606j51qcvwdd6kegr0/62cnd1259678467.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259678606j51qcvwdd6kegr0/62cnd1259678467.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259678606j51qcvwdd6kegr0/7fk001259678467.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/01/t1259678606j51qcvwdd6kegr0/7fk001259678467.ps (open in new window)

Parameters (Session):

par1 = FALSE ; par2 = 1.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = FALSE ; par2 = 1.0 ; 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')

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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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