R version 2.8.0 (2008-10-20)
Copyright (C) 2008 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(83.1,89.6,105.7,110.7,110.4,109,106,100.9,114.3,101.2,109.2,111.6,91.7,93.7,105.7,109.5,105.3,102.8,100.6,97.6,110.3,107.2,107.2,108.1,97.1,92.2,112.2,111.6,115.7,111.3,104.2,103.2,112.7,106.4,102.6,110.6,95.2,89,112.5,116.8,107.2,113.6,101.8,102.6,122.7,110.3,110.5,121.6,100.3,100.7,123.4,127.1,124.1,131.2,111.6,114.2,130.1,125.9,119,133.8,107.5,113.5,134.4,126.8,135.6,139.9,129.8,131,153.1,134.1,144.1,155.9,123.3,128.1,144.3,153,149.9,150.9,141,138.9,157.4,142.9,151.7,161,138.5,135.9,151.5,164,159.1,157,142.1,144.8,152.1,154.6,148.7,157.7,146.7)
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '0'
> par5 = '12'
> par4 = '1'
> par3 = '1'
> par2 = '0.1'
> par1 = 'FALSE'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> library(lattice)
> if (par1 == 'TRUE') par1 <- TRUE
> if (par1 == 'FALSE') par1 <- FALSE
> par2 <- as.numeric(par2) #Box-Cox lambda transformation parameter
> par3 <- as.numeric(par3) #degree of non-seasonal differencing
> par4 <- as.numeric(par4) #degree of seasonal differencing
> par5 <- as.numeric(par5) #seasonal period
> par6 <- as.numeric(par6) #degree (p) of the non-seasonal AR(p) polynomial
> par7 <- as.numeric(par7) #degree (q) of the non-seasonal MA(q) polynomial
> par8 <- as.numeric(par8) #degree (P) of the seasonal AR(P) polynomial
> par9 <- as.numeric(par9) #degree (Q) of the seasonal MA(Q) polynomial
> armaGR <- function(arima.out, names, n){
+ try1 <- arima.out$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)))
[[1]]
           [,1]       [,2]
[1,] -0.6211937 -0.9970398
[2,] -0.6096443  0.0000000
[3,]         NA         NA
[4,]         NA         NA

[[2]]
     [,1]    [,2]
[1,]    0 0.06903
[2,]    0      NA
[3,]   NA      NA
[4,]   NA      NA

[[3]]
[[3]][[1]]

Call:
arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, 
    method = "ML")

Coefficients:
          ma1     sma1
      -0.6212  -0.9970
s.e.   0.0753   0.5421

sigma^2 estimated as 3.416e-05:  log likelihood = 300.16,  aic = -594.32

[[3]][[2]]

Call:
arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, 
    method = "ML")

Coefficients:
          ma1     sma1
      -0.6212  -0.9970
s.e.   0.0753   0.5421

sigma^2 estimated as 3.416e-05:  log likelihood = 300.16,  aic = -594.32


$aic
[1] -594.3207 -582.0962

> postscript(file="/var/www/html/rcomp/tmp/1p7f21228766973.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> resid <- arimaSelectplot(selection)
> dev.off()
null device 
          1 
> resid
Time Series:
Start = 1 
End = 97 
Frequency = 1 
 [1]  8.982542e-04  4.108218e-04  2.910209e-04  2.234253e-04  1.778387e-04
 [6]  1.460928e-04  1.209586e-04  9.840956e-05  1.062670e-04  7.712706e-05
[11]  8.167997e-05 -8.139705e-04 -5.512542e-03 -5.050127e-03 -7.263058e-03
[16] -5.422494e-03 -7.370106e-03 -5.794155e-03 -2.865032e-03  3.787024e-04
[21] -8.173454e-05  1.048254e-02 -2.072288e-03 -2.807420e-03  1.205014e-02
[26] -5.866424e-03  3.432271e-03 -3.902541e-03  5.043530e-03  4.359921e-04
[31] -5.109214e-03  7.377963e-04 -4.137401e-03 -2.856442e-04 -9.866994e-03
[36]  1.693714e-03  4.250230e-03 -8.541229e-03  4.871529e-03  4.711680e-03
[41] -8.739277e-03  6.117585e-03 -6.062572e-03  1.408433e-03  1.030552e-02
[46]  1.128216e-03 -8.781757e-04  7.953548e-03  1.377935e-03  2.191809e-03
[51]  5.090780e-03  3.365636e-03  1.894899e-03  9.896267e-03 -9.221415e-03
[56]  4.755667e-04  7.832955e-04  6.982321e-03 -5.310728e-03  6.526134e-03
[61] -2.896343e-03  6.680750e-03  2.426408e-03 -1.135096e-02  6.324808e-03
[66]  7.458311e-03  4.793720e-03  6.034274e-03  8.269891e-03 -4.588060e-03
[71]  8.376022e-03  7.715828e-03 -3.846681e-03  2.478795e-03 -7.214164e-03
[76]  2.386988e-03 -4.824220e-04 -1.034159e-03  4.835075e-04 -7.854469e-04
[81] -1.279555e-03 -3.618662e-03  5.445008e-03  2.604966e-03  6.931590e-03
[86] -2.213613e-04 -9.218046e-03  3.497880e-03 -1.086060e-03 -4.403962e-03
[91] -6.708798e-03  9.363078e-05 -1.233564e-02  7.360620e-03 -4.010727e-03
[96] -3.297481e-03  1.473484e-02
> postscript(file="/var/www/html/rcomp/tmp/24je61228766973.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> acf(resid,length(resid)/2, main='Residual Autocorrelation Function')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/3hzy21228766973.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> pacf(resid,length(resid)/2, main='Residual Partial Autocorrelation Function')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/4i5by1228766973.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> cpgram(resid, main='Residual Cumulative Periodogram')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/51n441228766973.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> hist(resid, main='Residual Histogram', xlab='values of Residuals')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/6kaei1228766973.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> densityplot(~resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
> dev.off()
null device 
          1 
> postscript(file="/var/www/html/rcomp/tmp/7lptx1228766973.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> qqnorm(resid, main='Residual Normal Q-Q Plot')
> qqline(resid)
> dev.off()
null device 
          1 
> ncols <- length(selection[[1]][1,])
> nrows <- length(selection[[2]][,1])-1
> 
> #Note: the /var/www/html/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/html/rcomp/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="/var/www/html/rcomp/tmp/8zvmm1228766973.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="/var/www/html/rcomp/tmp/96x531228766973.tab") 
> 
> system("convert tmp/1p7f21228766973.ps tmp/1p7f21228766973.png")
> system("convert tmp/24je61228766973.ps tmp/24je61228766973.png")
> system("convert tmp/3hzy21228766973.ps tmp/3hzy21228766973.png")
> system("convert tmp/4i5by1228766973.ps tmp/4i5by1228766973.png")
> system("convert tmp/51n441228766973.ps tmp/51n441228766973.png")
> system("convert tmp/6kaei1228766973.ps tmp/6kaei1228766973.png")
> system("convert tmp/7lptx1228766973.ps tmp/7lptx1228766973.png")
> 
> 
> proc.time()
   user  system elapsed 
  1.689   1.040   3.909