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

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> x <- c(31.58,27.88,27.32,28.89,28.05,28.73,32.00,34.53,33.47,34.09,35.47,34.59,34.32,32.78,28.38,29.18,28.62,28.20,29.33,29.72,26.29,26.82,27.64,27.10,27.05,26.02,25.76,25.94,24.97,21.74,18.16,16.95,16.46,16.44,18.20,16.44,15.70,13.94,12.23,14.75,14.62,15.04,15.50,16.10,15.44,15.14,15.42,15.69,17.57,18.42,17.96,18.39,17.63,17.95,17.79,17.73,18.99,19.83,20.23,20.24,21.12,21.25,21.80,21.84,22.21,22.64,23.54,23.78,23.65,23.93,24.77,26.26,27.69,29.54,29.31,29.26,28.69,26.16,27.12,29.40,30.99,32.96,32.20,31.67,32.49,33.66,32.44,34.38,32.36,30.73,30.31,27.26,25.05,22.33,18.26,18.30,16.00,14.36,14.98,16.88,16.56,13.31,9.61,9.34,7.89,1.71,0.81,0.71)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '0.0'
> par1 = '12'
> #'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!)
> 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
      0.2592  0.0154  0.1148
s.e.  0.1042  0.1122  0.1103

sigma^2 estimated as 0.003752:  log likelihood = 130.44,  aic = -252.89
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 2.891183 2.864052 2.857030 2.852989 2.848721 2.846746 2.845705 2.844915
 [9] 2.844468 2.844220 2.844059 2.843962

$se
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 0.06125686 0.09849763 0.12828397 0.15715122 0.18358101 0.20748178
 [7] 0.22954230 0.25001323 0.26909978 0.28702572 0.30395815 0.32002909

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 2.771119 2.670997 2.605593 2.544973 2.488902 2.440082 2.395802 2.354889
 [9] 2.317032 2.281650 2.248301 2.216705
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 3.011246 3.057107 3.108467 3.161006 3.208539 3.253411 3.295608 3.334941
 [9] 3.371904 3.406791 3.439817 3.471219
> 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$pred))
  [1] 31.58000 27.88000 27.32000 28.89000 28.05000 28.73000 32.00000 34.53000
  [9] 33.47000 34.09000 35.47000 34.59000 34.32000 32.78000 28.38000 29.18000
 [17] 28.62000 28.20000 29.33000 29.72000 26.29000 26.82000 27.64000 27.10000
 [25] 27.05000 26.02000 25.76000 25.94000 24.97000 21.74000 18.16000 16.95000
 [33] 16.46000 16.44000 18.20000 16.44000 15.70000 13.94000 12.23000 14.75000
 [41] 14.62000 15.04000 15.50000 16.10000 15.44000 15.14000 15.42000 15.69000
 [49] 17.57000 18.42000 17.96000 18.39000 17.63000 17.95000 17.79000 17.73000
 [57] 18.99000 19.83000 20.23000 20.24000 21.12000 21.25000 21.80000 21.84000
 [65] 22.21000 22.64000 23.54000 23.78000 23.65000 23.93000 24.77000 26.26000
 [73] 27.69000 29.54000 29.31000 29.26000 28.69000 26.16000 27.12000 29.40000
 [81] 30.99000 32.96000 32.20000 31.67000 32.49000 33.66000 32.44000 34.38000
 [89] 32.36000 30.73000 30.31000 27.26000 25.05000 22.33000 18.26000 18.30000
 [97] 18.01460 17.53242 17.40974 17.33954 17.26568 17.23162 17.21370 17.20010
[105] 17.19241 17.18815 17.18538 17.18371
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 97 
End = 108 
Frequency = 1 
 [1] 0.06508591 0.10864793 0.14585273 0.18404250 0.22095392 0.25602033
 [7] 0.28987751 0.32263191 0.35437811 0.38529502 0.41551310 0.44513641
> postscript(file="/var/www/html/rcomp/tmp/1izzs1229514762.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.se <- array(0, dim=fx)
> perf.mse <- 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$pred[i]
+ perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
+ perf.se[i] = (x[nx+i] - forecast$pred[i])^2
+ perf.mse[i] = perf.mse[i] + perf.se[i]
+ 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 = perf.mape / fx
> perf.mse = perf.mse / fx
> perf.rmse = sqrt(perf.mse)
> postscript(file="/var/www/html/rcomp/tmp/2cfsb1229514762.ps",horizontal=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[1:12] <- x[(nx+1):lx]
> lines(dum, lty=1)
> lines(ub,lty=3)
> lines(lb,lty=3)
> dev.off()
null device 
          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,'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/www/html/rcomp/tmp/3xts11229514762.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.mape[i],4))
+ a<-table.element(a,round(perf.se[i],4))
+ a<-table.element(a,round(perf.mse[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/www/html/rcomp/tmp/45s3v1229514762.tab") 
> 
> system("convert tmp/1izzs1229514762.ps tmp/1izzs1229514762.png")
> system("convert tmp/2cfsb1229514762.ps tmp/2cfsb1229514762.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.585   0.300   0.859