R version 2.15.2 (2012-10-26) -- "Trick or Treat"
Copyright (C) 2012 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i686-pc-linux-gnu (32-bit)

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> x <- c(54.3,55.9,63.9,64,60.7,67.8,70.5,76.6,76.2,71.8,67.8,69.7,76.7,74.2,75.8,84.3,84.9,84.4,89.4,88.5,76.5,71.4,72.1,75.8,66.6,71.7,75.4,80.9,80.7,85,91.5,87.7,95.3,102.4,114.2,111.7,113.7,118.8,129,136.4,155,166,168.7,145.5,127.3,91.5,69,54,56.3,54.2,59.3,63.4,73.3,86.7,81.3,89.6,85.3,92.4,96.8,93.6,97.6,94.2,99.9,106.4,96,94.9,94.8,95.9,96.2,103.1,106.9,114.2,118.2,123.9,137.1,146.2,136.4,133.2,135.9,127.1,128.5,126.6,132.6,130.9)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> par1 = '24'
> par10 <- 'FALSE'
> par9 <- '0'
> par8 <- '0'
> par7 <- '1'
> par6 <- '3'
> par5 <- '12'
> par4 <- '0'
> par3 <- '1'
> par2 <- '1'
> par1 <- '24'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: Wessa P., (2009), ARIMA Forecasting (v1.0.5) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_arimaforecasting.wasp/
> #Source of accompanying publication: 
> #Technical description: 
> par1 <- as.numeric(par1) #cut off periods
> par2 <- as.numeric(par2) #lambda
> 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) #p
> par7 <- as.numeric(par7) #q
> par8 <- as.numeric(par8) #P
> par9 <- as.numeric(par9) #Q
> if (par10 == 'TRUE') par10 <- TRUE
> if (par10 == 'FALSE') par10 <- FALSE
> if (par2 == 0) x <- log(x)
> if (par2 != 0) x <- x^par2
> lx <- length(x)
> first <- lx - 2*par1
> nx <- lx - par1
> nx1 <- nx + 1
> fx <- lx - nx
> if (fx < 1) {
+ fx <- par5
+ nx1 <- lx + fx - 1
+ first <- lx - 2*fx
+ }
> first <- 1
> if (fx < 3) fx <- round(lx/10,0)
> (arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML'))

Call:
arima(x = x[1:nx], order = c(par6, par3, par7), seasonal = list(order = c(par8, 
    par4, par9), period = par5), include.mean = par10, method = "ML")

Coefficients:
         ar1      ar2      ar3      ma1
      1.2728  -0.1445  -0.2847  -0.8937
s.e.  0.1682   0.2262   0.1333   0.1509

sigma^2 estimated as 52.31:  log likelihood = -200.98,  aic = 411.96
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 61 
End = 84 
Frequency = 1 
 [1] 92.68832 90.73787 89.29802 88.00678 87.12662 86.60285 86.43097 86.53845
 [9] 86.84921 87.27813 87.74856 88.19687 88.57740 88.86303 89.04396 89.12464
[17] 89.11988 89.05065 88.94025 88.81110 88.68237 88.56863 88.47922 88.41850

$se
Time Series:
Start = 61 
End = 84 
Frequency = 1 
 [1]  7.232351 12.320305 17.493176 21.839469 25.302105 27.836797 29.569010
 [8] 30.670745 31.329910 31.709148 31.930000 32.071928 32.182968 32.293179
[15] 32.424711 32.595932 32.820759 33.106092 33.450106 33.842793 34.268601
[22] 34.710044 35.151048 35.579188

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 61 
End = 84 
Frequency = 1 
 [1] 78.51291 66.59007 55.01139 45.20142 37.53450 32.04273 28.47571 26.42379
 [9] 25.44258 25.12820 25.16576 25.33589 25.49878 25.56840 25.49152 25.23661
[17] 24.79119 24.16271 23.37804 22.47922 21.51592 20.53694 19.58316 18.68329
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 61 
End = 84 
Frequency = 1 
 [1] 106.8637 114.8857 123.5846 130.8121 136.7187 141.1630 144.3862 146.6531
 [9] 148.2558 149.4281 150.3314 151.0579 151.6560 152.1577 152.5964 153.0127
[17] 153.4486 153.9386 154.5025 155.1430 155.8488 156.6003 157.3753 158.1537
> if (par2 == 0) {
+ x <- exp(x)
+ forecast$pred <- exp(forecast$pred)
+ lb <- exp(lb)
+ ub <- exp(ub)
+ }
> if (par2 != 0) {
+ x <- x^(1/par2)
+ forecast$pred <- forecast$pred^(1/par2)
+ lb <- lb^(1/par2)
+ ub <- ub^(1/par2)
+ }
> if (par2 < 0) {
+ olb <- lb
+ lb <- ub
+ ub <- olb
+ }
> (actandfor <- c(x[1:nx], forecast$pred))
 [1]  54.30000  55.90000  63.90000  64.00000  60.70000  67.80000  70.50000
 [8]  76.60000  76.20000  71.80000  67.80000  69.70000  76.70000  74.20000
[15]  75.80000  84.30000  84.90000  84.40000  89.40000  88.50000  76.50000
[22]  71.40000  72.10000  75.80000  66.60000  71.70000  75.40000  80.90000
[29]  80.70000  85.00000  91.50000  87.70000  95.30000 102.40000 114.20000
[36] 111.70000 113.70000 118.80000 129.00000 136.40000 155.00000 166.00000
[43] 168.70000 145.50000 127.30000  91.50000  69.00000  54.00000  56.30000
[50]  54.20000  59.30000  63.40000  73.30000  86.70000  81.30000  89.60000
[57]  85.30000  92.40000  96.80000  93.60000  92.68832  90.73787  89.29802
[64]  88.00678  87.12662  86.60285  86.43097  86.53845  86.84921  87.27813
[71]  87.74856  88.19687  88.57740  88.86303  89.04396  89.12464  89.11988
[78]  89.05065  88.94025  88.81110  88.68237  88.56863  88.47922  88.41850
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 61 
End = 84 
Frequency = 1 
 [1] 0.07802871 0.13577909 0.19589658 0.24815666 0.29040613 0.32143050
 [7] 0.34211128 0.35441753 0.36073916 0.36331149 0.36388062 0.36364019
[13] 0.36333160 0.36340400 0.36414274 0.36573423 0.36827654 0.37176701
[19] 0.37609638 0.38106491 0.38641952 0.39190000 0.39728028 0.40239529
> postscript(file="/var/wessaorg/rcomp/tmp/1idcw1354196398.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$pred , lwd=2 , col ='white')
> box()
> par(opar)
> dev.off()
null device 
          1 
> prob.dec <- array(NA, dim=fx)
> prob.sdec <- array(NA, dim=fx)
> prob.ldec <- array(NA, dim=fx)
> prob.pval <- array(NA, dim=fx)
> perf.pe <- array(0, dim=fx)
> perf.mape <- array(0, dim=fx)
> perf.mape1 <- array(0, dim=fx)
> perf.se <- array(0, dim=fx)
> perf.mse <- array(0, dim=fx)
> perf.mse1 <- array(0, dim=fx)
> perf.rmse <- array(0, dim=fx)
> for (i in 1:fx) {
+ locSD <- (ub[i] - forecast$pred[i]) / 1.96
+ perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i]
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD)
+ prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD)
+ prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD)
+ prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD)
+ }
> perf.mape[1] = abs(perf.pe[1])
> perf.mse[1] = abs(perf.se[1])
> for (i in 2:fx) {
+ perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i])
+ perf.mape1[i] = perf.mape[i] / i
+ perf.mse[i] = perf.mse[i-1] + perf.se[i]
+ perf.mse1[i] = perf.mse[i] / i
+ }
> perf.rmse = sqrt(perf.mse1)
> postscript(file="/var/wessaorg/rcomp/tmp/2obpb1354196398.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub)))
> dum <- forecast$pred
> dum[1:par1] <- x[(nx+1):lx]
> lines(dum, lty=1)
> lines(ub,lty=3)
> lines(lb,lty=3)
> dev.off()
null device 
          1 
> 
> #Note: the /var/wessaorg/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/wessaorg/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'time',1,header=TRUE)
> a<-table.element(a,'Y[t]',1,header=TRUE)
> a<-table.element(a,'F[t]',1,header=TRUE)
> a<-table.element(a,'95% LB',1,header=TRUE)
> a<-table.element(a,'95% UB',1,header=TRUE)
> a<-table.element(a,'p-value<br />(H0: Y[t] = F[t])',1,header=TRUE)
> a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE)
> a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE)
> mylab <- paste('P(F[t]>Y[',nx,sep='')
> mylab <- paste(mylab,'])',sep='')
> a<-table.element(a,mylab,1,header=TRUE)
> a<-table.row.end(a)
> for (i in (nx-par5):nx) {
+ a<-table.row.start(a)
+ a<-table.element(a,i,header=TRUE)
+ a<-table.element(a,x[i])
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.element(a,'-')
+ a<-table.row.end(a)
+ }
> for (i in 1:fx) {
+ a<-table.row.start(a)
+ a<-table.element(a,nx+i,header=TRUE)
+ a<-table.element(a,round(x[nx+i],4))
+ a<-table.element(a,round(forecast$pred[i],4))
+ a<-table.element(a,round(lb[i],4))
+ a<-table.element(a,round(ub[i],4))
+ a<-table.element(a,round((1-prob.pval[i]),4))
+ a<-table.element(a,round((1-prob.dec[i]),4))
+ a<-table.element(a,round((1-prob.sdec[i]),4))
+ a<-table.element(a,round((1-prob.ldec[i]),4))
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/3zawi1354196398.tab") 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Univariate ARIMA Extrapolation Forecast Performance',7,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'time',1,header=TRUE)
> a<-table.element(a,'% S.E.',1,header=TRUE)
> a<-table.element(a,'PE',1,header=TRUE)
> a<-table.element(a,'MAPE',1,header=TRUE)
> a<-table.element(a,'Sq.E',1,header=TRUE)
> a<-table.element(a,'MSE',1,header=TRUE)
> a<-table.element(a,'RMSE',1,header=TRUE)
> a<-table.row.end(a)
> for (i in 1:fx) {
+ a<-table.row.start(a)
+ a<-table.element(a,nx+i,header=TRUE)
+ a<-table.element(a,round(perc.se[i],4))
+ a<-table.element(a,round(perf.pe[i],4))
+ a<-table.element(a,round(perf.mape1[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse1[i],4))
+ a<-table.element(a,round(perf.rmse[i],4))
+ a<-table.row.end(a)
+ }
> a<-table.end(a)
> table.save(a,file="/var/wessaorg/rcomp/tmp/4rxqy1354196398.tab") 
> 
> try(system("convert tmp/1idcw1354196398.ps tmp/1idcw1354196398.png",intern=TRUE))
character(0)
> try(system("convert tmp/2obpb1354196398.ps tmp/2obpb1354196398.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.766   0.347   2.096