R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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> x <- c(100.01,103.84,104.48,95.43,104.80,108.64,105.65,108.42,115.35,113.64,115.24,100.33,101.29,104.48,99.26,100.11,103.52,101.18,96.39,97.56,96.39,85.10,79.77,79.13,80.84,82.75,92.55,96.60,96.92,95.32,98.52,100.22,104.91,103.10,97.13,103.42,111.72,118.11,111.62,100.22,102.03,105.76,107.68,110.77,105.44,112.26,114.07,117.90,124.72,126.42,134.73,135.79,143.36,140.37,144.74,151.98,150.92,163.38,154.43,146.66,157.95,162.10,180.42,179.57,171.58,185.43,190.64,203.00,202.36,193.41,186.17,192.24,209.60,206.41,209.82,230.37,235.80,232.07,244.64,242.19,217.48,209.39,211.73,221.00,203.11,214.71,224.19,238.04,238.36,246.24,259.87,249.97,266.48,282.98,306.31,301.73,314.62,332.62,355.51,370.32,408.13,433.58,440.51,386.29,342.84,254.97,203.42,170.09,174.03,167.85,177.01,188.19,211.20,240.91,230.26,251.25,241.66)
> par10 = 'FALSE'
> par9 = '0'
> par8 = '0'
> par7 = '1'
> par6 = '3'
> par5 = '12'
> par4 = '0'
> par3 = '2'
> 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      ar3      ma1
      0.3960  -0.1278  -0.0969  -0.9808
s.e.  0.1062   0.1276   0.1284   0.0412

sigma^2 estimated as 122.4:  log likelihood = -395.26,  aic = 800.53
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 106 
End = 117 
Frequency = 1 
 [1] 334.4646 344.5283 356.3659 363.1492 365.9171 367.5691 369.7825 372.7501
 [9] 376.0526 379.3370 382.4982 385.5806

$se
Time Series:
Start = 106 
End = 117 
Frequency = 1 
 [1] 11.06650 19.18226 25.16920 29.35200 32.65942 35.66201 38.59475 41.48845
 [9] 44.31371 47.05393 49.71642 52.31822

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 106 
End = 117 
Frequency = 1 
 [1] 312.7743 306.9310 307.0342 305.6192 301.9046 297.6716 294.1368 291.4327
 [9] 289.1977 287.1112 285.0540 283.0369
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 106 
End = 117 
Frequency = 1 
 [1] 356.1550 382.1255 405.6975 420.6791 429.9295 437.4667 445.4283 454.0674
 [9] 462.9074 471.5627 479.9424 488.1243
> 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$pred))
  [1] 100.0100 103.8400 104.4800  95.4300 104.8000 108.6400 105.6500 108.4200
  [9] 115.3500 113.6400 115.2400 100.3300 101.2900 104.4800  99.2600 100.1100
 [17] 103.5200 101.1800  96.3900  97.5600  96.3900  85.1000  79.7700  79.1300
 [25]  80.8400  82.7500  92.5500  96.6000  96.9200  95.3200  98.5200 100.2200
 [33] 104.9100 103.1000  97.1300 103.4200 111.7200 118.1100 111.6200 100.2200
 [41] 102.0300 105.7600 107.6800 110.7700 105.4400 112.2600 114.0700 117.9000
 [49] 124.7200 126.4200 134.7300 135.7900 143.3600 140.3700 144.7400 151.9800
 [57] 150.9200 163.3800 154.4300 146.6600 157.9500 162.1000 180.4200 179.5700
 [65] 171.5800 185.4300 190.6400 203.0000 202.3600 193.4100 186.1700 192.2400
 [73] 209.6000 206.4100 209.8200 230.3700 235.8000 232.0700 244.6400 242.1900
 [81] 217.4800 209.3900 211.7300 221.0000 203.1100 214.7100 224.1900 238.0400
 [89] 238.3600 246.2400 259.8700 249.9700 266.4800 282.9800 306.3100 301.7300
 [97] 314.6200 332.6200 355.5100 370.3200 408.1300 433.5800 440.5100 386.2900
[105] 342.8400 334.4646 344.5283 356.3659 363.1492 365.9171 367.5691 369.7825
[113] 372.7501 376.0526 379.3370 382.4982 385.5806
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 106 
End = 117 
Frequency = 1 
 [1] 0.03308722 0.05567688 0.07062740 0.08082629 0.08925361 0.09702122
 [7] 0.10437147 0.11130368 0.11783913 0.12404258 0.12997819 0.13568687
> postscript(file="/var/www/html/rcomp/tmp/1sqp01261158612.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2znav1261158612.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/3ange1261158612.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/4i12x1261158612.tab") 
> 
> try(system("convert tmp/1sqp01261158612.ps tmp/1sqp01261158612.png",intern=TRUE))
character(0)
> try(system("convert tmp/2znav1261158612.ps tmp/2znav1261158612.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  0.667   0.320   0.850