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(130.3,130.9,104.7,115.2,124.5,112.3,127.5,120.6,117.5,117.7,120.4,125,131.6,121.1,114.2,112.1,127,116.8,112,129.7,113.6,115.7,119.5,125.8,129.6,128,112.8,101.6,123.9,118.8,109.1,130.6,112.4,111,116.2,119.8,117.2,127.3,107.7,97.5,120.1,110.6,111.3,119.8,105.5,108.7,128.7,119.5,121.1,128.4,108.8,107.5,125.6,102.9,107.5,120.4,104.3,100.6,121.9,112.7,124.9,123.9,102.2,104.9,109.8,98.9,107.3,112.6,104,110.6,100.8,103.8,117,108.4,95.5,96.9,103.9,101.1,100.6,104.3,98,99.5,97.4,105.6,117.5,107.4,97.8,91.5,107.7,100.1,96.6,106.8,98,98.6)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '0'
> par6 = '3'
> par5 = '12'
> par4 = '1'
> par3 = '0'
> 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     sar1     sar2     sma1
      0.1117  0.2332  0.6545  -0.0564  -0.4782  -0.9534
s.e.  0.0957  0.0903  0.1003   0.1314   0.1188   0.4111

sigma^2 estimated as 16.78:  log likelihood = -215.09,  aic = 444.18
> (forecast <- predict(arima.out,fx))
$pred
Time Series:
Start = 83 
End = 94 
Frequency = 1 
 [1] 100.33295 106.18329 106.95744 108.06327  93.93102  87.83082 108.60657
 [8]  98.01994  95.83377 108.55851  93.70043  92.13434

$se
Time Series:
Start = 83 
End = 94 
Frequency = 1 
 [1] 4.395367 4.418126 4.530121 5.458138 5.524827 5.718052 6.179807 6.284542
 [9] 6.495230 6.785125 6.912202 7.113987

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 83 
End = 94 
Frequency = 1 
 [1] 91.71803 97.52377 98.07841 97.36532 83.10236 76.62343 96.49415 85.70224
 [9] 83.10312 95.25967 80.15251 78.19093
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 83 
End = 94 
Frequency = 1 
 [1] 108.9479 114.8428 115.8365 118.7612 104.7597  99.0382 120.7190 110.3376
 [9] 108.5644 121.8574 107.2483 106.0778
> 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$pred))
 [1] 130.30000 130.90000 104.70000 115.20000 124.50000 112.30000 127.50000
 [8] 120.60000 117.50000 117.70000 120.40000 125.00000 131.60000 121.10000
[15] 114.20000 112.10000 127.00000 116.80000 112.00000 129.70000 113.60000
[22] 115.70000 119.50000 125.80000 129.60000 128.00000 112.80000 101.60000
[29] 123.90000 118.80000 109.10000 130.60000 112.40000 111.00000 116.20000
[36] 119.80000 117.20000 127.30000 107.70000  97.50000 120.10000 110.60000
[43] 111.30000 119.80000 105.50000 108.70000 128.70000 119.50000 121.10000
[50] 128.40000 108.80000 107.50000 125.60000 102.90000 107.50000 120.40000
[57] 104.30000 100.60000 121.90000 112.70000 124.90000 123.90000 102.20000
[64] 104.90000 109.80000  98.90000 107.30000 112.60000 104.00000 110.60000
[71] 100.80000 103.80000 117.00000 108.40000  95.50000  96.90000 103.90000
[78] 101.10000 100.60000 104.30000  98.00000  99.50000 100.33295 106.18329
[85] 106.95744 108.06327  93.93102  87.83082 108.60657  98.01994  95.83377
[92] 108.55851  93.70043  92.13434
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 83 
End = 94 
Frequency = 1 
 [1] 0.04380782 0.04160848 0.04235442 0.05050873 0.05881792 0.06510303
 [7] 0.05690086 0.06411493 0.06777601 0.06250201 0.07376917 0.07721319
> postscript(file="/var/www/html/rcomp/tmp/17d4w1229955621.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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/2nd4e1229955622.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/35eaq1229955622.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/4k9zv1229955622.tab") 
> 
> system("convert tmp/17d4w1229955621.ps tmp/17d4w1229955621.png")
> system("convert tmp/2nd4e1229955622.ps tmp/2nd4e1229955622.png")
> 
> 
> proc.time()
   user  system elapsed 
  3.850   0.613   4.224