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(98.8,100.5,110.4,96.4,101.9,106.2,81,94.7,101,109.4,102.3,90.7,96.2,96.1,106,103.1,102,104.7,86,92.1,106.9,112.6,101.7,92,97.4,97,105.4,102.7,98.1,104.5,87.4,89.9,109.8,111.7,98.6,96.9,95.1,97,112.7,102.9,97.4,111.4,87.4,96.8,114.1,110.3,103.9,101.6,94.6,95.9,104.7,102.8,98.1,113.9,80.9,95.7,113.2,105.9,108.8,102.3,99,100.7,115.5,100.7,109.9,114.6,85.4,100.5,114.8,116.5,112.9,102,106,105.3,118.8,106.1,109.3,117.2,92.5,104.2,112.5,122.4,113.3,100,110.7,112.8,109.8,117.3,109.1,115.9,96,99.8,116.8,115.7,99.4,94.3)
> par10 = 'FALSE'
> par9 = '1'
> par8 = '2'
> par7 = '0'
> par6 = '3'
> 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     ar2     ar3    sar1     sar2     sma1
      0.0031  0.3344  0.5425  0.2682  -0.1798  -1.0000
s.e.  0.1122  0.1127  0.1346  0.2008   0.2044   0.3231

sigma^2 estimated as 8.676:  log likelihood = -160.47,  aic = 334.94
> (forecast <- predict(arima.out,par1))
$pred
Time Series:
Start = 73 
End = 96 
Frequency = 1 
 [1] 104.62905 104.88902 116.59471 106.35570 109.02521 114.25729  90.19100
 [8] 100.52479 114.58779 117.50135 109.84481 101.38312 102.82346 103.22838
[15] 113.87395 106.23487 105.26193 112.77926  89.09921  98.47876 113.03158
[22] 114.61215 107.23378 100.19228

$se
Time Series:
Start = 73 
End = 96 
Frequency = 1 
 [1] 3.198509 3.198235 3.365745 3.772124 3.787621 3.952217 4.083447 4.119278
 [9] 4.226451 4.283139 4.323370 4.386754 4.774133 4.808600 4.918542 5.066216
[17] 5.105878 5.194154 5.262499 5.299323 5.357782 5.388387 5.417177 5.453962

> (lb <- forecast$pred - 1.96 * forecast$se)
Time Series:
Start = 73 
End = 96 
Frequency = 1 
 [1]  98.35997  98.62048 109.99785  98.96233 101.60147 106.51094  82.18744
 [8]  92.45100 106.30395 109.10640 101.37101  92.78508  93.46616  93.80352
[15] 104.23361  96.30509  95.25440 102.59872  78.78471  88.09209 102.53032
[22] 104.05091  96.61612  89.50252
> (ub <- forecast$pred + 1.96 * forecast$se)
Time Series:
Start = 73 
End = 96 
Frequency = 1 
 [1] 110.89813 111.15756 123.19157 113.74906 116.44895 122.00363  98.19455
 [8] 108.59857 122.87164 125.89630 118.31862 109.98116 112.18076 112.65323
[15] 123.51429 116.16466 115.26945 122.95981  99.41371 108.86544 123.53283
[22] 125.17339 117.85145 110.88205
> 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$pred))
 [1]  98.80000 100.50000 110.40000  96.40000 101.90000 106.20000  81.00000
 [8]  94.70000 101.00000 109.40000 102.30000  90.70000  96.20000  96.10000
[15] 106.00000 103.10000 102.00000 104.70000  86.00000  92.10000 106.90000
[22] 112.60000 101.70000  92.00000  97.40000  97.00000 105.40000 102.70000
[29]  98.10000 104.50000  87.40000  89.90000 109.80000 111.70000  98.60000
[36]  96.90000  95.10000  97.00000 112.70000 102.90000  97.40000 111.40000
[43]  87.40000  96.80000 114.10000 110.30000 103.90000 101.60000  94.60000
[50]  95.90000 104.70000 102.80000  98.10000 113.90000  80.90000  95.70000
[57] 113.20000 105.90000 108.80000 102.30000  99.00000 100.70000 115.50000
[64] 100.70000 109.90000 114.60000  85.40000 100.50000 114.80000 116.50000
[71] 112.90000 102.00000 104.62905 104.88902 116.59471 106.35570 109.02521
[78] 114.25729  90.19100 100.52479 114.58779 117.50135 109.84481 101.38312
[85] 102.82346 103.22838 113.87395 106.23487 105.26193 112.77926  89.09921
[92]  98.47876 113.03158 114.61215 107.23378 100.19228
> (perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
Time Series:
Start = 73 
End = 96 
Frequency = 1 
 [1] 0.03056999 0.03049161 0.02886705 0.03546706 0.03474078 0.03459050
 [7] 0.04527555 0.04097774 0.03688396 0.03645183 0.03935889 0.04326907
[13] 0.04643038 0.04658215 0.04319286 0.04768882 0.04850641 0.04605593
[19] 0.05906337 0.05381184 0.04740075 0.04701410 0.05051745 0.05443495
> postscript(file="/var/www/html/rcomp/tmp/1kc6e1260544390.ps",horizontal=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> opar <- par(mar=c(4,4,2,2),las=1)
> ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
> plot(x,ylim=ylim,type='n',xlim=c(first,lx))
> usr <- par('usr')
> rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
> rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
> abline(h= (-3:3)*2 , col ='gray', lty =3)
> polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
> lines(nx1:lx, lb , lty=2)
> lines(nx1:lx, ub , lty=2)
> lines(x, lwd=2)
> lines(nx1:lx, forecast$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.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/www/html/rcomp/tmp/2piq61260544390.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: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/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/3f4f21260544390.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/www/html/rcomp/tmp/4q7ic1260544390.tab") 
> 
> system("convert tmp/1kc6e1260544390.ps tmp/1kc6e1260544390.png")
> system("convert tmp/2piq61260544390.ps tmp/2piq61260544390.png")
> 
> 
> proc.time()
   user  system elapsed 
  2.248   0.383   2.426