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(0.42,0.74,1.02,1.51,1.86,1.59,1.03,0.44,0.82,0.86,0.57,0.59,0.95,0.98,1.23,1.17,0.84,0.74,0.65,0.91,1.19,1.3,1.53,1.94,1.79,1.95,2.26,2.04,2.16,2.75,2.79,2.88,3.36,2.97,3.1,2.49,2.2,2.25,2.09,2.79,3.14,2.93,2.65,2.67,2.26,2.35,2.13,2.18,2.9,2.63,2.67,1.81,1.33,0.88,1.28,1.26,1.26,1.29,1.1,1.37,1.21,1.74,1.76,1.48,1.04,1.62,1.49,1.79,1.8,1.58,1.86,1.74,1.59,1.26,1.13,1.92,2.61,2.26,2.41,2.26,2.03,2.86,2.55,2.27,2.26,2.57,3.07,2.76,2.51,2.87,3.14,3.11,3.16,2.47,2.57,2.89,2.63,2.38,1.69,1.96,2.19,1.87,1.6,1.63,1.22,1.21,1.49,1.64,1.66,1.77,1.82,1.78,1.28,1.29,1.37,1.12,1.51,2.24,2.94,3.09)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '0'
> par7 = '1'
> par6 = '2'
> par5 = '12'
> par4 = '0'
> par3 = '1'
> par2 = '1'
> 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      ma1     sma1
      0.6517  -0.2479  -0.5215  -0.9996
s.e.  0.2308   0.0984   0.2221   0.5146

sigma^2 estimated as 0.05986:  log likelihood = -14.98,  aic = 39.97
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 1.874903 1.768299 1.917496 1.707385 1.576406 1.654606 1.629610 1.532894
 [9] 1.941724 2.095270 1.948006 1.785274

$se
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.2577615 0.3880043 0.4606189 0.5073345 0.5452593 0.5808694 0.6155564
 [8] 0.6490597 0.6810812 0.7116564 0.7410041 0.7692888

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 1.3696903 1.0078104 1.0146826 0.7130092 0.5076978 0.5161021 0.4231194
 [8] 0.2607371 0.6068044 0.7004231 0.4956375 0.2774682
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 2.380115 2.528787 2.820309 2.701761 2.645114 2.793110 2.836100 2.805051
 [9] 3.276643 3.490116 3.400374 3.293080
> 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$pred))
  [1] 0.420000 0.740000 1.020000 1.510000 1.860000 1.590000 1.030000 0.440000
  [9] 0.820000 0.860000 0.570000 0.590000 0.950000 0.980000 1.230000 1.170000
 [17] 0.840000 0.740000 0.650000 0.910000 1.190000 1.300000 1.530000 1.940000
 [25] 1.790000 1.950000 2.260000 2.040000 2.160000 2.750000 2.790000 2.880000
 [33] 3.360000 2.970000 3.100000 2.490000 2.200000 2.250000 2.090000 2.790000
 [41] 3.140000 2.930000 2.650000 2.670000 2.260000 2.350000 2.130000 2.180000
 [49] 2.900000 2.630000 2.670000 1.810000 1.330000 0.880000 1.280000 1.260000
 [57] 1.260000 1.290000 1.100000 1.370000 1.210000 1.740000 1.760000 1.480000
 [65] 1.040000 1.620000 1.490000 1.790000 1.800000 1.580000 1.860000 1.740000
 [73] 1.590000 1.260000 1.130000 1.920000 2.610000 2.260000 2.410000 2.260000
 [81] 2.030000 2.860000 2.550000 2.270000 2.260000 2.570000 3.070000 2.760000
 [89] 2.510000 2.870000 3.140000 3.110000 3.160000 2.470000 2.570000 2.890000
 [97] 2.630000 2.380000 1.690000 1.960000 2.190000 1.870000 1.600000 1.630000
[105] 1.220000 1.210000 1.490000 1.640000 1.874903 1.768299 1.917496 1.707385
[113] 1.576406 1.654606 1.629610 1.532894 1.941724 2.095270 1.948006 1.785274
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 109 
End = 120 
Frequency = 1 
 [1] 0.1374799 0.2194223 0.2402190 0.2971413 0.3458876 0.3510620 0.3777324
 [8] 0.4234211 0.3507612 0.3396491 0.3803912 0.4309079
> postscript(file="/var/www/html/rcomp/tmp/1ac3k1229616099.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2xyt41229616099.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/3ykm91229616099.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/4g3sg1229616100.tab") 
> 
> system("convert tmp/1ac3k1229616099.ps tmp/1ac3k1229616099.png")
> system("convert tmp/2xyt41229616099.ps tmp/2xyt41229616099.png")
> 
> 
> proc.time()
   user  system elapsed 
  0.848   0.323   0.972