R version 2.13.0 (2011-04-13)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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> x <- c(12.008,9.169,8.788,8.417,8.247,8.197,8.236,8.253,7.733,8.366,8.626,8.863,10.102,8.463,9.114,8.563,8.872,8.301,8.301,8.278,7.736,7.973,8.268,9.476,11.100,8.962,9.173,8.738,8.459,8.078,8.411,8.291,7.810,8.616,8.312,9.692,9.911,8.915,9.452,9.112,8.472,8.230,8.384,8.625,8.221,8.649,8.625,10.443,10.357,8.586,8.892,8.329,8.101,7.922,8.120,7.838,7.735,8.406,8.209,9.451,10.041,9.411,10.405,8.467,8.464,8.102,7.627,7.513,7.510,8.291,8.064,9.383,9.706,8.579,9.474,8.318,8.213,8.059,9.111,7.708,7.680,8.014,8.007,8.718,9.486,9.113,9.025,8.476,7.952,7.759,7.835,7.600,7.651,8.319,8.812,8.630)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '1'
> par6 = '1'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> 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     ma1     sar1     sar2    sma1
      0.4528  0.0388  -1.1653  -0.2109  0.7994
s.e.  0.2305  0.2362   0.6224   0.3871  0.7244

sigma^2 estimated as 0.1599:  log likelihood = -33.29,  aic = 78.58
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 73 
End = 96 
Frequency = 1 
 [1] 10.212049  9.025752  9.677417  8.286233  8.203278  7.964581  7.790373
 [8]  7.533146  7.518612  8.374379  8.068227  9.186769  9.845833  9.194959
[15] 10.158325  8.446102  8.420734  8.082314  7.701949  7.577300  7.555616
[22]  8.301280  8.093797  9.429749

$se
Time Series:
Start = 73 
End = 96 
Frequency = 1 
 [1] 0.4021926 0.4479142 0.4567239 0.4585094 0.4588746 0.4589495 0.4589648
 [8] 0.4589677 0.4589670 0.4589606 0.4589291 0.4587754 0.5228080 0.5371888
[15] 0.5400901 0.5406831 0.5408046 0.5408295 0.5408346 0.5408357 0.5408359
[22] 0.5408358 0.5408350 0.5408315

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 73 
End = 96 
Frequency = 1 
 [1] 9.423751 8.147840 8.782238 7.387554 7.303883 7.065040 6.890802 6.633570
 [9] 6.619037 7.474816 7.168726 8.287570 8.821129 8.142069 9.099748 7.386363
[17] 7.360757 7.022288 6.641913 6.517263 6.495578 7.241242 7.033761 8.369719
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 73 
End = 96 
Frequency = 1 
 [1] 11.000346  9.903663 10.572596  9.184911  9.102672  8.864122  8.689944
 [8]  8.432723  8.418187  9.273942  8.967728 10.085969 10.870536 10.247849
[15] 11.216901  9.505841  9.480711  9.142339  8.761984  8.637338  8.615655
[22]  9.361319  9.153834 10.489779
> 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$pred))
 [1] 12.008000  9.169000  8.788000  8.417000  8.247000  8.197000  8.236000
 [8]  8.253000  7.733000  8.366000  8.626000  8.863000 10.102000  8.463000
[15]  9.114000  8.563000  8.872000  8.301000  8.301000  8.278000  7.736000
[22]  7.973000  8.268000  9.476000 11.100000  8.962000  9.173000  8.738000
[29]  8.459000  8.078000  8.411000  8.291000  7.810000  8.616000  8.312000
[36]  9.692000  9.911000  8.915000  9.452000  9.112000  8.472000  8.230000
[43]  8.384000  8.625000  8.221000  8.649000  8.625000 10.443000 10.357000
[50]  8.586000  8.892000  8.329000  8.101000  7.922000  8.120000  7.838000
[57]  7.735000  8.406000  8.209000  9.451000 10.041000  9.411000 10.405000
[64]  8.467000  8.464000  8.102000  7.627000  7.513000  7.510000  8.291000
[71]  8.064000  9.383000 10.212049  9.025752  9.677417  8.286233  8.203278
[78]  7.964581  7.790373  7.533146  7.518612  8.374379  8.068227  9.186769
[85]  9.845833  9.194959 10.158325  8.446102  8.420734  8.082314  7.701949
[92]  7.577300  7.555616  8.301280  8.093797  9.429749
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 73 
End = 96 
Frequency = 1 
 [1] 0.03938413 0.04962625 0.04719482 0.05533388 0.05593796 0.05762381
 [7] 0.05891436 0.06092642 0.06104411 0.05480534 0.05688104 0.04993871
[13] 0.05309942 0.05842210 0.05316725 0.06401570 0.06422298 0.06691519
[19] 0.07022050 0.07137577 0.07158064 0.06515088 0.06682093 0.05735375
> postscript(file="/var/wessaorg/rcomp/tmp/10cev1323162864.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/22xlf1323162864.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/3u6jh1323162864.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/43iym1323162864.tab") 
> 
> try(system("convert tmp/10cev1323162864.ps tmp/10cev1323162864.png",intern=TRUE))
character(0)
> try(system("convert tmp/22xlf1323162864.ps tmp/22xlf1323162864.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  3.617   0.585   4.198