R version 2.6.0 (2007-10-03)
Copyright (C) 2007 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(102.86,102.12,100.74,100.96,101.01,100.41,100.35,99.33,98.66,98.69,98.61,96.41,96.3,96.12,97.32,101.78,102.28,101.12,104.55,107.4,108.41,109.43,110.34,115.06,113.13,116.56,121.39,119.12,123.31,128.57,127.71,125.68,133.8,130.97,129.99,124,118.63,121.86,119.97,125.03,130.09,126.65,121.7,119.24,122.63,116.66,114.12,113.11,112.61,113.4,115.18,121.01,119.44,116.68,117.07,117.41,119.58,120.92,117.09,116.77,119.39,122.49,124.08,118.29,112.94,113.79,114.43,118.7,120.36,118.27,118.34,117.82,117.65,118.18,121.02,124.78,131.16,130.14,131.75,134.73,135.35,140.32,136.35,131.6,128.9,133.89,138.25,146.23,144.76,149.3,156.8,159.08,165.12,163.14,153.43,151.01)
> par9 = '1'
> par8 = '2'
> par7 = '1'
> par6 = '3'
> par5 = '1'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = 'TRUE'
> #'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$order[3]
+ coeff <- matrix(NA, nrow=nrc, ncol=nrc)
+ pval <- matrix(NA, nrow=nrc, ncol=nrc)
+ mylist <- rep(list(NULL), nrc)
+ names  <- NULL
+ if(order[1] > 0) names <- paste('ar',1:order[1],sep='')
+ if(order[3] > 0) names <- c( names , paste('ma',1:order[3],sep='') )
+ if(seasonal$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)
+ 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]      [,3]        [,4]      [,5]       [,6]
[1,] -0.3908962 0.10881611 0.3392287 -0.02378532 0.6859325 -0.5068459
[2,] -0.3950357 0.10735664 0.3386122  0.00000000 0.6836609 -0.5052268
[3,] -0.4196392 0.09636033 0.3336363  0.00000000 0.6683869 -0.4952525
[4,] -0.4715119 0.00000000 0.2810579  0.00000000 0.7135642 -0.4621309
[5,]         NA         NA        NA          NA        NA         NA
[6,]         NA         NA        NA          NA        NA         NA
[7,]         NA         NA        NA          NA        NA         NA
            [,7]
[1,] -0.02378532
[2,] -0.04097519
[3,]  0.00000000
[4,]  0.00000000
[5,]          NA
[6,]          NA
[7,]          NA

[[2]]
        [,1]    [,2]    [,3]    [,4]    [,5]    [,6]    [,7]
[1,] 0.26618 0.61739 0.02231 0.97704 0.00501 0.00667 0.97704
[2,] 0.24072 0.62396 0.02287      NA 0.00412 0.00552 0.93450
[3,] 0.00738 0.59734 0.01792      NA 0.00001 0.00054      NA
[4,] 0.00028      NA 0.00824      NA 0.00000 0.00059      NA
[5,]      NA      NA      NA      NA      NA      NA      NA
[6,]      NA      NA      NA      NA      NA      NA      NA
[7,]      NA      NA      NA      NA      NA      NA      NA

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

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

Coefficients:
          ar1     ar2     ar3      ma1    sar1     sar2     sma1
      -0.3909  0.1088  0.3392  -0.0238  0.6859  -0.5068  -0.0238
s.e.   0.3493  0.2171  0.1458   0.8243  0.2383   0.1824   0.8243

sigma^2 estimated as 10.77:  log likelihood = -247.82,  aic = 511.64

[[3]][[2]]

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

Coefficients:
          ar1     ar2     ar3      ma1    sar1     sar2     sma1
      -0.3909  0.1088  0.3392  -0.0238  0.6859  -0.5068  -0.0238
s.e.   0.3493  0.2171  0.1458   0.8243  0.2383   0.1824   0.8243

sigma^2 estimated as 10.77:  log likelihood = -247.82,  aic = 511.64

[[3]][[3]]

Call:
arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, 
    fixed = last.arma$next.vector, method = "ML")

Coefficients:
          ar1     ar2     ar3  ma1    sar1     sar2     sma1
      -0.3950  0.1074  0.3386    0  0.6837  -0.5052  -0.0410
s.e.   0.3345  0.2182  0.1462    0  0.2322   0.1776   0.4971

sigma^2 estimated as 10.77:  log likelihood = -247.82,  aic = 509.64

[[3]][[4]]

Call:
arima(x = series, order = order, seasonal = seasonal, include.mean = include.mean, 
    fixed = last.arma$next.vector, method = "ML")

Coefficients:
          ar1     ar2     ar3  ma1    sar1     sar2  sma1
      -0.4196  0.0964  0.3336    0  0.6684  -0.4953     0
s.e.   0.1531  0.1818  0.1384    0  0.1455   0.1380     0

sigma^2 estimated as 10.77:  log likelihood = -247.83,  aic = 507.65

[[3]][[5]]
NULL

[[3]][[6]]
NULL

[[3]][[7]]
NULL


$aic
[1] 511.6423 509.6431 507.6503 505.8700

Warning message:
In arima(series, order = order, seasonal = seasonal, include.mean = include.mean,  :
  some AR parameters were fixed: setting transform.pars = FALSE
> postscript(file="/var/www/html/rcomp/tmp/1cq1i1196438007.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 = 96 
Frequency = 1 
 [1]  0.10285994 -0.70444872 -1.19519064  0.44691142 -0.12246935 -0.62089417
 [7] -0.03794632 -0.81260793 -0.41412797 -0.03386083 -0.01554261 -2.30427480
[13]  0.47703432 -0.29226400  1.34785686  3.77455586 -0.11203432 -0.84331925
[19]  3.74396820  2.41218495  0.12913854  0.60968666  1.39374029  4.48518330
[25] -3.35285566  4.42499956  3.44940241 -2.26985769  3.99778193  4.57247527
[31] -1.25305993 -2.64647137  9.30963084 -4.80778100 -0.20976949 -6.79362956
[37] -2.06361120  2.07893823 -2.66567420  5.35436332  3.42773242 -2.53000583
[43] -4.67082563 -0.74754439  3.67782103 -8.23963320 -0.80172033 -0.90651742
[49]  0.81770755 -0.65579599  2.12754950  5.75414176 -2.77868745 -1.56734395
[55]  0.71411476  0.74031643  1.06258022  0.59218742 -3.40284372  0.65328198
[61]  2.48797421  2.52187383  0.25604839 -5.40255238 -3.39973025  1.50801149
[67] -0.08294800  3.26238914  0.64042004 -1.00361796  0.49598110 -0.24414341
[73] -0.31862306 -0.13419921  3.07757222  3.02404311  5.80457660 -2.21518448
[79]  2.79851633  2.25675689  0.62898104  3.83680646 -4.86510983 -2.95574620
[85] -2.67743905  6.11161131  1.57364639  7.47553909 -2.93351778  6.90361698
[91]  5.64630827  1.72051651  4.50594252 -2.63433691 -8.07787467 -1.44961560
> postscript(file="/var/www/html/rcomp/tmp/2a64n1196438007.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/354vd1196438007.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/4m7bh1196438007.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/5uqok1196438007.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/6t8i31196438007.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/7wqjh1196438007.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> qqnorm(resid, main='Residual Normal Q-Q Plot')
> dev.off()
null device 
          1 
> ncols <- length(selection[[1]][1,])
> nrows <- length(selection[[2]][,1])-1
> 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/8euvh1196438007.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/9ml5w1196438007.tab") 
> 
> system("convert tmp/1cq1i1196438007.ps tmp/1cq1i1196438007.png")
> system("convert tmp/2a64n1196438007.ps tmp/2a64n1196438007.png")
> system("convert tmp/354vd1196438007.ps tmp/354vd1196438007.png")
> system("convert tmp/4m7bh1196438007.ps tmp/4m7bh1196438007.png")
> system("convert tmp/5uqok1196438007.ps tmp/5uqok1196438007.png")
> system("convert tmp/6t8i31196438007.ps tmp/6t8i31196438007.png")
> system("convert tmp/7wqjh1196438007.ps tmp/7wqjh1196438007.png")
> 
> 
> proc.time()
   user  system elapsed 
  2.343   1.129   2.800