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(3.5300,3.4900,3.5100,3.5300,3.5400,3.5600,3.5800,3.6100,3.5600,3.5600,3.6100,3.6100,3.6200,3.6300,3.6500,3.7200,3.7200,3.7300,3.7300,3.7200,3.7200,3.7000,3.7100,3.7200,3.7200,3.7300,3.7300,3.7300,3.7500,3.7400,3.8300,3.9400,3.9500,3.9700,3.9900,3.9900,4.0000,4.0000,4.0000,3.9900,3.9600,3.9800,4.0300,4.0800,4.0700,4.0700,4.0500,4.0500,4.0500,4.0600,4.0700,4.0900,4.0900,4.1100,4.1700,4.1800,4.1600,4.1600,4.1700,4.1700,4.1900,4.2000,4.1900,4.1800,4.1200,4.1200,4.1300,4.1500,4.1200,4.1100,4.1000,4.1000)
> par9 = '1'
> par8 = '2'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1.3'
> 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$order[3]
+ coeff <- matrix(NA, nrow=nrc, ncol=nrc)
+ pval <- matrix(NA, nrow=nrc, ncol=nrc)
+ mylist <- rep(list(NULL), nrc)
+ names  <- NULL
+ if(order[1] > 0) names <- paste('ar',1:order[1],sep='')
+ if(order[3] > 0) names <- c( names , paste('ma',1:order[3],sep='') )
+ if(seasonal$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,] -0.51601227  0.238082332 0.08141501 0.8660560 0.5143660 0.2085220
[2,] -0.53004469  0.229999613 0.07446885 0.8735424 0.1830251 0.3061141
[3,] -0.53156104  0.207446706 0.00000000 0.8935596 0.1607144 0.3152671
[4,]  0.10500984 -0.001552165 0.00000000 0.2775507 0.0000000 0.3356245
[5,]  0.05090025  0.000000000 0.00000000 0.3310145 0.0000000 0.3388037
[6,]          NA           NA         NA        NA        NA        NA
[7,]          NA           NA         NA        NA        NA        NA
           [,7]
[1,] -0.3596949
[2,]  0.0000000
[3,]  0.0000000
[4,]  0.0000000
[5,]  0.0000000
[6,]         NA
[7,]         NA

[[2]]
        [,1]    [,2]    [,3]    [,4]    [,5]    [,6]    [,7]
[1,] 0.01863 0.11890 0.55174 0.00000 0.51543 0.47529 0.67255
[2,] 0.01066 0.12621 0.58223 0.00000 0.15561 0.01800      NA
[3,] 0.00631 0.14272      NA 0.00000 0.17966 0.01378      NA
[4,] 0.00774 0.28310      NA 0.01126      NA 0.00000      NA
[5,] 0.03889      NA      NA 0.00000      NA 0.00000      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
      -0.5160  0.2381  0.0814  0.8661  0.5144  0.2085  -0.3597
s.e.   0.2137  0.1506  0.1361  0.1669  0.7864  0.2904   0.8471

sigma^2 estimated as 0.002158:  log likelihood = 115.27,  aic = -214.53

[[3]][[2]]

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

Coefficients:
          ar1     ar2     ar3     ma1    sar1    sar2     sma1
      -0.5160  0.2381  0.0814  0.8661  0.5144  0.2085  -0.3597
s.e.   0.2137  0.1506  0.1361  0.1669  0.7864  0.2904   0.8471

sigma^2 estimated as 0.002158:  log likelihood = 115.27,  aic = -214.53

[[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
      -0.5300  0.2300  0.0745  0.8735  0.1830  0.3061     0
s.e.   0.2016  0.1485  0.1347  0.1542  0.1274  0.1261     0

sigma^2 estimated as 0.002176:  log likelihood = 115.18,  aic = -216.36

[[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
      -0.5316  0.2074    0  0.8936  0.1607  0.3153     0
s.e.   0.1884  0.1398    0  0.1315  0.1185  0.1246     0

sigma^2 estimated as 0.002187:  log likelihood = 115.03,  aic = -218.06

[[3]][[5]]

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
      0.1050  -0.0016    0  0.2776     0  0.3356     0
s.e.  0.0382   0.0014    0  0.1065     0  0.0037     0

sigma^2 estimated as 0.002291:  log likelihood = 113.63,  aic = -217.26

[[3]][[6]]
NULL

[[3]][[7]]
NULL


$aic
[1] -214.5326 -216.3622 -218.0637 -217.2625 -219.1359

Warning messages:
1: In arima(series, order = order, seasonal = seasonal, include.mean = include.mean,  :
  some AR parameters were fixed: setting transform.pars = FALSE
2: In arima(series, order = order, seasonal = seasonal, include.mean = include.mean,  :
  some AR parameters were fixed: setting transform.pars = FALSE
3: 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/10gz61196865516.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 = 72 
Frequency = 1 
 [1]  0.005153554 -0.066636704  0.060079935  0.015273475  0.009951793
 [6]  0.031232274  0.023475631  0.043701502 -0.107543406  0.039363076
[11]  0.078741433 -0.031281351  0.026826843  0.008686078  0.031811463
[16]  0.114182920 -0.044952814  0.030836973 -0.010463225 -0.015239694
[21]  0.006137353 -0.038021246  0.032600181  0.008157871  0.005930929
[26]  0.041872681 -0.028908579 -0.003305903  0.034483770 -0.045057271
[31]  0.177564498  0.129336222 -0.004570984  0.035441731 -0.006530457
[36]  0.001101471  0.012987135 -0.011420073 -0.008993010 -0.061028085
[41] -0.035272018  0.048731149  0.081492245  0.072482498 -0.050846986
[46]  0.029288129 -0.055565626  0.013809627 -0.003225119  0.014196865
[51]  0.014461615  0.033571092 -0.026412384  0.054938977  0.040793142
[56] -0.069799117 -0.021545777 -0.002405715  0.008718371 -0.003147823
[61]  0.034205837  0.006994745 -0.023976286 -0.004578066 -0.097093331
[66]  0.024204196 -0.018678463  0.013164466 -0.057423264  0.001646775
[71] -0.005024970  0.002054002
> postscript(file="/var/www/html/rcomp/tmp/2dh8m1196865516.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/3qhor1196865516.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/4pn5d1196865516.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/5pegh1196865516.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/6lshp1196865516.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/7033a1196865516.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/84djw1196865516.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/9i63c1196865516.tab") 
> 
> system("convert tmp/10gz61196865516.ps tmp/10gz61196865516.png")
> system("convert tmp/2dh8m1196865516.ps tmp/2dh8m1196865516.png")
> system("convert tmp/3qhor1196865516.ps tmp/3qhor1196865516.png")
> system("convert tmp/4pn5d1196865516.ps tmp/4pn5d1196865516.png")
> system("convert tmp/5pegh1196865516.ps tmp/5pegh1196865516.png")
> system("convert tmp/6lshp1196865516.ps tmp/6lshp1196865516.png")
> system("convert tmp/7033a1196865516.ps tmp/7033a1196865516.png")
> 
> 
> proc.time()
   user  system elapsed 
  7.744   1.983   9.356